... I believe they regain health on a timed basis, as long as their well-fed.  As you say, I can't prove it.
... 
 Yes I think so.
I do not believe working your villagers hurts them or weakens them, or prevents recuperation.  
... 
 Yes, it is!! If I look at the 
ldwlog.txt  folders of my VV2 game:
"Tue Jun 26 11:05:08 2007: Tiki FijLap collected some crops. Crops remaining: 1077
Tue Jun 26 11:05:08 2007: Current food available to eat: 107596
Tue Jun 26 11:05:08 2007: 
Lakia PapKon was injured while researching. Remaining health: 90Tue Jun 26 11:05:08 2007: Research successful. Tech points generated: 30"
But they may recover their health: 

"Tue Jun 26 11:05:08 2007: Current food available to eat: 106880
Tue Jun 26 11:05:08 2007: 
Papa HeriCol healed one point. Current health: 99Tue Jun 26 11:05:08 2007: Hebe AgaSyl is going to do some food gathering."
This one is also very interesting: 

"Tue Jun 26 11:05:08 2007: Research successful. Tech points generated: 16
Tue Jun 26 11:05:08 2007: Research successful. Tech points generated: 16
Tue Jun 26 11:05:08 2007: 
Fire assisted researchers. Extra point gained."
Ok, it is in VV2 (we don't have anything like that in the VV3 folders 

 ) But I think it's the same in VV3!