There would be numerous checks and balances that would need to be in place, obviously, but it's an interesting idea. Just imagine, you die so you click on the healer henchie and take control of healing until your character is rezzed or the healer you control dies.
A few things I can think of:
1. No henchie inventory or drops.
2. Henchies can't zone.
3. The crappy "Rush the oncoming army alone" Warrior dies and takes control of the henchie Monk? Um......no. Griefing potential x100 would need to be addressed somehow. Maybe allow the team leader to allow or disallow AI displacement with a party checkbox or something so he can stop griefers?
Basically, it's not the most well thought out concept but, hey, that's what Forums are for, no?

Discuss, theorize, debunk, etc.

-Beat