can they send you a check for your winnings?

It would be a good idea and seems more convenient for the winners. Pay pal is not reliable and they require lots of personal info including social security number for new accounts that want to transfer money to their bank account.  

Sadly a reading of the rules strongly implies we have to give all our info over to pay pal and create an account even if we do not want one.  If you have an account  set up some time in the past you may be able to get by without giving them so much info.