Why would the USMC sponsor a game? I mean I take it you mean like recruiters and stuff... people that want to get their foot in the door or potential recruits or something.
I know for sure they would be willing to come out to a game and talk to people, and I'm sure most of them would be more than willing to play (if you lent them a gun). Still I don't see them wanting to be responsible for hosting a sports event they almost certianly know nothing about (none of my recruiters knew what airsoft was). Combined with the legal responsibilities that they would have to assume and the cost of sponsoring a game, I'm sure that the high command would give it a no-go.
If you are going to invite military out to play, make sure and get in touch with all the guys that are on RA too. I know that there are now like 5 guys on RA at my recruiting station (metrocenter).