That would probably be uglier than having the entity be in full control.
I mean, he'd probably be begging you to kill him, whenever he got the chance to speak.
That would be a sight to see.
I can see it now. Lambert is possessed, and knowing that the people he promoted and the ball he got rolling with declaring the Nevarran Accord to be void, knows his life is forfeit if he is found. So he hides. We the Inquisitor can find him and put him in the party, occasionally talking to him or Cole. Cole asks us to kill Lambert, and Lambert is desperate to find out if he can be unpossessed, and decides to see if he can make himself tranquil, only for Cole to point out that that wouldn't work since he's already possessed.
Eventually we have a choice to take Lambert to Fiona and ask her to help, or to take him to the Chantry and have them execute him and Cole.
*cackling madly* IT'LL BE BRILLIANT, BRILLIANT BRILLIANT!!!