It's possible, but I think you give parents too much credit for rationality. The kind who send their kids off to school without lunch/lunch money are so utterly self-absorbed that I don't think it makes a whit of difference if a perceptive teacher helps the kid. They'll not notice anyway. Gambling/alcohol/crack/whatever else the parents do will take their undivided attention.
I was only giving MY parents credit for behavior I had observed in them. They both felt that the 'government' owed them something; any money that came their way through what ever source they felt was their just due. If I'd have come home with a new coat, my step-father would have noticed; potential pawn material.