I think so (I had a friend rejected from USNA for this reason, but he was told he could apply for Marine option), but you should check with the ROTC unit you are interested in. They could give you a definitive yes or no. You would be restricted in your job choices once commissioned however: you couldn't go pilot/NFO for example.
I have no idea about specific MOSs- I am in NROTC but a Navy option. Try asking the Marine Officer Instructor at an NROTC school you are interested in.