I did In Your Heart Shall Burn, finally (had to sleep before work) and I think it almost makes more sense having Dorian show up then. He's actively fighting and has an explanation for it, and he can't help you as he's admittedly exhausted from out running the army. His conversation after that almost sounds tailored to that introduction versus meeting during the mage quest (though I miss out on him promising to protect my PC

).
Playing a Dalish First, running into Cole while dealing with the Envy demon underscores my boy's belief that spirits and demons are different, something he already agreed with Solas about, and he instantly recognized Envy for what it was, which is a good contrast to Cole. Then saving Dorian at the gates (because it's clear he wasn't going to last much longer since he was about to collapse) gives his recruitment a little more oomph. Suspecting him of being a spy, and Dorian's "Well, let me help for now and hang me later" attitude is well received.
I dunno, it just definitely *feels* much different for them versus my Dalish hunter stumbling into Redcliff village where he's so out of his element and naive to magic, while my mage chose Templars, believing the mages to be too unstable and powerful to approach.
Yeah, it's all the same in the end, but the flavor is subtly different. Yay for roleplaying? Lol