Not likely, Philadelphia made 424,470,400 dimes that year with no mintmark, so if you got it in change your odds are about half as good as winning the powerball lottery. If you pulled it out of a proof set (not a mint set), then your odds are considerably better.
You can send any coin to get graded.. That has to do with the condition of the coin.. If you think you have a Mint Error or a Variety then you would send a the coin to get Attributed. That's a different service provided by the third party graders.