A mask will certainly "contain" sound and affect the way it is picked up by your mics.
Whenever I have performed in full-body puppets it has been synced to a recording, or in the case of
Little Shop of Horrors I was syncing to the live voice of another actor speaking/singing the role. It takes some getting used to, but if you have good teamwork skills, it loses nothing in spontaneity. As long as I was listening to him, and he was watching me were ready for any needed ad-libbing.
In fact, I was just reading an article about Jennifer Barnhart in Ave. Q, (
http://www.broadway.com/gen/Buzz_Story.aspx?ci=553755) and when Rick Lyon wrenched his ankle, she puppeteered Trekkie, Nicky etc while Rick did the voices live from a position where he could see her.