I would think
a) bloody hell they're desparate for help - is there anything else I can do
b) do they really think that a prize draw will motivate people - I'd be doing this to help them/my dcs out, not for a flipping prize (esp if there's no mention of the actual prizes - my cynical mind says one soap-on-a-rope & a bottle of blue nun)
I'd personally prefer a note saying we're desperate for help - have you thought about whether you can help out with any of the following tasks:
blah, blah, blah
I like the idea of options if you work ft - perhaps options for those with older/younger kids (eg if you have a young baby, we're always happy for them to accompany you - or somthing else if you're not!
Perhaps also asking if people have grandparents who might like to be involved?