You know, I've been thinking about that a lot, and it very well may have done. Lyrium strengthens one's connection to the Fade, but possession is like dedicated broadband, to the extent that tranquil in the vicinity can shake it off for a while.
With the Veil torn wide, it's interesting to think what that might do to templar abilities, as well as their lyrium dependency.
Yes, it's very interesting, and I wonder how it will affect Cullen's lyrium addiction, if the Fade has something to do with it.
But I also thought that the addiction could be more physiological, and maybe the spirit simply restored the receptors responsible for it, when it healed the body. And pretty much undone the addiction, like it never happened.
P.S. Ok, now I'm totally enjoying the idea of Cullen becoming addicted to Inquisitor's magical Hand of Fade instead of lyrium

*dirty thoughts*
Inquisitor: *panicking* What if Cullen doesn't love me? What if he loves just my hand, because it prevents him from losing his mind?
Cassandra:

Varric: Ah, come on, Reverence, what's not to love about you? You are totally his type. He loves heroic powerful women who do crazy things, trust me!
Leliana: At least he does until demons come.
Cassandra: Just stay away from red lyrium.
Leliana: And demons.
Sera: How exactly do you apply your magical hand to him?
Solas: Yes! Tell me more! For science!
Cullen: (enters the room) Good evening!
Everybody: (instantly shuts up)
Cullen: I'm sorry, did I interrupt something?
Cassandra: No, not at all. I should go.
Cullen: You were talking about me?
Everybody: Nope.
Inquisitor: Yes.
Everybody: (facepalms)