I would strongly advise against such a set up. At best you could install a version per OS and be sure to make one the primary and back up the other from that one.
Linux and windows use very different file systems and different hooks. The mysql version for windows and the version for Linux though they will act the same for the most part will be configured and have very different files that make them work.
The other alternative is to go out and buy a Pentium I or pentium II and install an OS it can handle (psst go linux or BSD) LAMP (Linux Apache MySQL Perl,Python,PHP).
Then your scripts on your local box can access a single data set on the cheapy MySQL box.
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