At least a bit.
I don't think winning the lottery in itself would make anyone properly happy but I can't see how it's possible to be happy if you're worrying about how to keep a roof over your head or where food will come from at the end of the week. We were poor but we were happy must really depend on just how poor you were, mustn't it?
My Grandad, who grew up very poor and became quite well off used to say "Money can't buy you happiness but it makes being miserable a damn sight more comfortable"