Our motorcycle club does one of these every month at our meetings. The money is much smaller (usually between $30 and $50-so the winner gets between $15 and $25). The most I have ever seen donated is the $0.50 to make it an even winnings. So, for example, if the total take was $31 and the winner was entitled to $15.50, the winner might say "Just give me the $15 and donate the $0.50." However, that is not expected or requested-and it happens only about 1/2 of the time. I am the treasurer right now, and I always keep a couple of dollars in quarters in petty cash for just such occasions.
I have also seen lots and lots of these drawings as they are popular with bikers, so you see them at biker charity events and poker runs on a really regular basis. I have never seen someone get nagged to donate their prize back, though I have seen it done on rare occasions.
I would never, however, expect a winner to donate their prize back to the charity. And the most I would do is donate the change to make it an even amount.