Your examiner might if he or she learned of it. Except for credit unions, depository institutions generally are subject to similar rules relating to lotteries (which includes raffles of the type you describe). The FDIC's rules prohibit dealing in lottery tickets, and "dealing in" includes making the tickets.
It would not be difficult for anyone to make the connection between "making" tickets and paying for their printing, particularly with the attribution on the back of the tickets you've described.
It is different from donating a prize. Perhaps your bank should consider changing its future plans and start donating a prize rather than paying the cost of ticket printing.
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John S. Burnett
BankersOnline.com
Fighting for Compliance since 1976
Bankers' Threads User #8