Yes! Get out of my head! Haha.
Well with no military force left it would make perfect sense for the Divine to acquire a new army. I don't see Cullen straying from his religious beliefs and could quite easily see him taking up the spot of General for the new troops (whom I could only imagine being Templar's with the same belief system as Cullen).
So maybe that is what he has spent his time doing, recruiting new troops for the Divine and training them I which would bring him into association with Leliana and Cassandra). Once all hell breaks loose, well it's as you said above. Cullen and the army he is in charge off become part of the Inquisition when it is reinstated. So it is quite possible that we could have him from the very beginning.
Sorry if this is a little, I'm trying very hard to ignore my step son packing a tantrum
Hehe,this is pretty much what I had in mind! 
Although I also believe the theory that after the explosion the divine dies,which makes these three factions except perhaps Leliana's, scatter around and become more independent for a while,while they continue their efforts to complete the task they were given.
Until Cassandra and Leli decide to follow the back-up plan and reform the inquisition.Then we'll have to find them and recruit them or have Cassandra/Leli recruit them for us,although I'd prefer the first. xD
Although,I think that having them from the beginning is also highly possible.