Indeed, al-Baghdadi has certainly fulfilled what he calls his "duty to Usama bin Laden". The move to reestablish the khalifah could have substantial positive consequences for the group in the world of global jihad; at the same time, however, it could also have adverse effects.
Looking at the positive possibilities, this move could attract larger amounts of foreign jihadists to the cause of IS. While IS already has a large contingent of foreign fighters, with whole brigades made up of certain nationalities (of which, Australians make up the largest number of foreigners per capita), this move could further highlight to other foreigners that the IS is the more "exciting" and "successful" group.
Moreover, it could attract more defectors from al-Qaeda into the fold of IS. Being that both groups want to reestablish the khalifah and both share the same ideology, al-Qaeda (AQ) has never been successful in doing so. While AQ has held significant ground in Afghanistan, Pakistan, Mali, Yemen, and Somalia, none has never been as significant as ash-Sham. The Umayyad Caliphate, the largest of the caliphates and fifth largest empire in history, had its capital in Damascus. The mere fact that they have claimed to reestablish the khalifah in the same area of the center of the Umayyad Caliphate wields a huge propaganda and even religious significance. IS will undoubtedly use this as propaganda to attract more AQ defectors.
Even further than individual defectors of al-Qaeda, IS could potentially see entire groups within the al-Qaeda Network or the al-Qaeda sphere of influence switch teams. If this scenario were to actually become true, it is more likely that groups in or near the Levant stands the biggest chances of actually switching sides. Earlier in the year, Ayman al-Zawahiri, the emir of al-Qaeda, issued a statement entitled "The Liberation of the Circle of Inefficiency and Failure". In this statement, he explicitly mentioned three areas that are and should be the main destinations for jihad: Syria, Egypt and Chechnya. The omission of areas like Yemen, the Sahel, Somalia or the areas of Afghanistan and Pakistan (AfPak) could alienate some groups to the point of defection.
Switching over to the negative side of things, this move could further the jihadist infighting currently happening in Syria (and there have been some reports of small-scale infighting in Iraq). From the official statement of the creation of IS, "We clarify to the Muslims that with this declaration of khilāfah, it is incumbent upon all Muslims to pledge allegiance to the khalīfah Ibrāhīm and support him (may Allah preserve him)". This level of perceived arrogance is likely to further alienate the group from moderate Muslims and even enrage those jihadists who see this move as a power-grab and/or a premature move.
The aforementioned groups within the al-Qaeda Network or sphere of influence also has the possibility of not even occurring. Throughout the infighting, most groups within these two al-Qaeda-headed tiers remained relatively quiet about the fighting between ISIS and Jabhat al-Nusra, the official AQ group in Syria. Those groups who did comment on the infighting, like Mokhtar Belmokhtar's al-Mulathameen Brigade, often sided with Zawahiri rather than Baghdadi. Being that Nasir al-Wuhayshi, the emir of al-Qaeda in the Arabian Peninsula (AQAP) is also the general manager of the entirety of the AQ Network, I find it hard to think that AQAP will defect to IS. In the same light, the AfPak-based groups are so intertwined with al-Qaeda in the region it would make it hard for them to shift allegiance elsewhere.
Many state-actors in the region, namely Iraq, Iran, Lebanon, Israel, and Jordan (one might be able to argue Turkey, but they have been accused of supporting ISIS in the past), will undoubtedly see the reestablishment of the khalifah as an even bigger threat to their security coupled with the military advances of IS inside Iraq. Military action by state actors, while is already happening by Iraqi, sometimes Syrian and quite possibly Iranian troops, has a greater chance of happening now that Jordan, Lebanon, and Israel all feel threatened. If IS begins to take the fight to Lebanon and/or Jordan, like some analysts fear, it becomes almost a near certainty for more military action against IS.
Another downside that comes along with controlling large swaths of ground: Not being able to hold on to said ground for very long. Like al-Qaeda forces in Mali, or Somalia, or Yemen, or Iraq in the days of al-Qaeda in Iraq, or even like the Taliban in Afghanistan, IS will probably not be able to hold on to their khalifah for very long. Daveed Gartenstien-Ross of the Foundation for the Defense of Democracies says: "Although non-state militants are formidable, they have no real response to their enemies’ air-power advantage, and haven’t been able to hold territory against the advance of professional militaries".
When IS begins to lose ground, their propaganda value could begin to downgrade. Furthermore, the loss of ground could prompt IS to take a less egotistical approach to both the global jihad and al-Qaeda.
Relationship with Rivals:
Like the above paragraph implies, IS is now in a position where they will need to hold on to their captured territory. Despite having a number of grievances with various groups inside both Iraq and Syria, they might need to start relying on them to help. For instance, Ansar al-Islam (AAI), a group founded in 2001 that is within the al-Qaeda sphere of influence, is a regional rival of IS. However, AAI is taking part in the "blitzkrieg" led by IS. Even though they are rivals, IS needs AAI to relieve pressure from them to take over various northern cities and avoid the risk stretching themselves too thin. In return, AAI gets to take the fight to the Iraqi military and government with the backing of a strong, well-equipped group that has numerous other allies taking part in the fighting.
The same might happen with Jabhat al-Nusra (JN) in parts of Syria. For example, IS could promise JN to not attack them in (insert city here) if JN lets them take this road or that crossing. In the same light, JN could promise ISIS to help them (insert city here) if ISIS retreats from "this". While they have been fighting, both share a mutual goal here. Ideology can and has historically been put aside to further mutual goals between two opposing groups. Without some levels of coordination between the two (or any other al-Qaeda group in the region, like Ahrar ash-Sham or Ansar Sham or Sham al-Islam), victory cannot be achieved. These small agreements could, potentially, lead to larger agreements for reconciliation. Continuing to fight each other does no one good.
However, the "requirement" for all Muslims to swear bayah (allegiance) to Baghdadi certainly ups the chances of more infighting occurring in both Syria and Iraq. In fact, nine different groups and coalitions of Syrian rebel groups, including Jabhat al-Nusra, refused to swear allegiance to Baghdadi. Those groups in Iraq fighting alongside IS now have a serious choice to make: Swear allegiance or fight them.
While IS supporters will rejoice that Baghdadi has finally achieved what he set out to do, their jubilation may not last long. The reestablishment of the khalifah poses both positive and negative possibilities for the group from everyday, moderate Muslims, to jihadists, to other terrorist groups and even to state-actors. IS might also have to reach out to its rivals if it wishes to be successful at this reestablishment. One thing is for certain though: Only time will tell what happens.
Note: The picture above is allegedly the new flag of IS.
Note v2: I added an analysis of the refusal of allegiance by nine rebel groups in Syria.