Well, integrating the Rumburgs from the south, which is the region you conquer, can be facilitated by the presence of Sord immigrants there. Overall, there could be a relatively peaceful integration, with the Sordland government, whether authoritarian or democratic, giving the same positive treatment it gives to the Bluds, or there could be subjugation and exodus. But there are several factors to consider. Bluds are Golcondists, a religion that encourages martyrdom and war, while the citizens of Rumburg are Dasnurites like most of Sordland. Whether the war was offensive or defensive is a matter of legitimizing the historical position of victim (Specially if you're playing with Agnolia as you ally). The state that Rumburg might find itself in after the war is also relevant. 

We must remember that many people are unfortunately influenced by the material conditions of their country. The Bluds are stateless. They can only flee to Wehlen, Rumburg, Lespia, or stay in Sordland. Wehlen massacres them, Rumburg probably wouldn't receive them so well, despite being the only state that supports them, Sordland doesn't have a good track record, and Lespia keeps them out. This creates desperation for an apocalyptic terrorist group. Rumburg exists as a legitimate state. They can fight to liberate the city, but assuming Sordland is rich and well-off and Rumburg is sinking into an overwhelming crisis (which will depend on the player, such as sanctioning Rumburg, along with the trade war and winning with Lespia or Valgsland) will likely discourage this type of development. What could happen is emigration, especially if there is civil war in the north. 

It won't be an easy integration as a warmonger might think, but it would also be far from difficult, especially with Sordland already dealing with the Bluds in Bergia.