Poorly, I'd assume. On top of the opposing religious ideologies and one being mage and the other a templar, Cullen seems the practical sort and Dorian... does not. I fully expect Dorian to troll the crud out of Cullen. And if they're both available for the same type of Inquisitor as LI...? Oh my God, I expect things to get catty and mean if the Inquisitor starts a love-triangle.
I think it would depend, though. Initially, Cullen would probably be all *side eye* at Dorian, but I think Cullen would eventually be able to see that Dorian's not a terrible person.
I don't know how I think Cullen would react in a love triangle situation. I, in fact, shudder to think. 