Does a Morgan silver dollar have any worth if it has no mint mark?

Yes, check eBay for its prices you should be astonished.

More...Any U.S. coin before 1980 without a mint mark is perfectly normal. It simply means the coin was minted in Philadelphia.

As of 05/2009 Morgan dollars of any date and mint mark retail for at least $14 in the lowest grade, and possibly very much more.

Check the Related Link for specific values.