Yes, because Shariah does not allow a valid Caliph (whom al-Baghdadi is, btw - he meets all the qualifications including being Qurayshi, the first real Caliph since like the Abbasids) to recognise any borders or accept any peace treaties longer than 10 years.
It's the duty of the Caliph to wage Jihad and conquer as much as possible territory to be included in Dar al-Islam - should he not do so, he would no longer be worthy of bays'a [allegiance] of Muslims.
It's not so much lebensraum but rather territory that hasn't yet been occupied by the Ummah (basically the nation that is Muslim).
This is the hardcore Salafi doctrine by which people like Daeesh operate by and it's theologically valid, though batshit insane.
HOWEVER, only about 70-80% of Muslims are Sunnis and of those maybe 10-15% are Salafis.
So no, the "mohammedic brutalism" will not be carried with them - they've seen what life under a Caliphate is like and they want the hell out of there.
I can say this with some certainty as during my last 3 years in Beirut (which BTW has more Syrian refugees than ANY Western city) say that the Daeesh are a bunch of psychopathic foreign assholes led by an eloquent sociopath from Baghdad.