This depends on the mb and ma files. MB files are written in binary (MB = Maya Binary) MA Files are written in ASCCI (MA = Maya ASCCI).

If Linux and windows can understand the bianry code written to this files (this should be application specific), then it should work. For safety I would use MA Files to save as and then it should minimise any issues. With MA files you can go in and edit the information and change what is required to let them run in the OS you are using. This would have to be done everythime you change the OS.

I would ask this question in a LINUX forum also. I am a windows owner so I am using my limited knowledge of Linux. I have asked a buddy, who is a linux admin guy, so I will post for feelings on the subject.