This is a hypothetical situation, so let's say it happens.
Like, what if it was this or die and he still has his goals/cause to complete. Under most circumstances, i think he would just rather die but ...hypothetically. 
OK, then, I enjoy assumptions.
So let's also assume he doesn't know a way to reverse the joining and he's locked in. We really don't know what the Blight is all about, so it's hard to say what the effect would be on him. I can think of some scenarios:
1. He is corrupted into an archdemon. Part of him despises who he has become, but his mission is still The Most Important Thing, the sole focus of his existence. So being the trickster he is, he decides to make the most of the situation and rallies the darkspawn behind him to fulfill his goals. This marks the beginning of The Sixth Blight and the Grey Wardens are called to fight. It all ends in an epic standoff between Solas and the Hero of Ferelden. Unless you chose the Ultimate Sacrifice, in which case the standoff is between Solas and the Inquisitor.
2. He becomes a regular Grey Warden. This means he has lost his immortality and feels pressed for time to complete his mission. Using his ample knowledge and cunning, he quickly rises through the Grey Warden ranks, and rallies the Wardens behind him towards his ultimate goal. The Inquisition is called to stop him and it all ends in an epic standoff between Solas and The Inquisitor.
Uh, 'tis all I can think of in between experiments.