[quote=@Jinxer]
Sounds like great fun, I would like to put my name forwards for this.

I would probably be playing as a Mystic, although would there be Mystics recruited into The Division?  As a consultant, for example.
[/quote]

I'll be posting lore (when and if this takes off) which will sort of answer your question. 

The Division is an anti-void operation, and Mystics are basically part of the void themselves, which in theory puts these factions against each other. However, they do cooperate if they bump into each other somewhere, but it isn't premeditated. It would also be rather difficult for a Mystic to pursue a military career, and then join The Division, for various reasons.