No hands on (pun intended) experience here, but I'd factor into it the children's age, and strawberry jam on little fingers...
The idea of a family computer is great, but I sorta miss dinners where people actually interact with eachother. Wouldn't a device tend to disencourage that?
That's just me...it could always be on 'sleep' mode during meals.
Good idea for a post, and a good question.