First off, I'm not familiar with Sync, but a quick read of the overview suggests that your client will need to provide either a web service or RSS feed in order for the Sync runtime to obtain the data to be sync'd from the Java process.
The problems I see with your design is that there's typically more than one client but, semantically, a single backend - the MySQL database in this case. I suspect this would lead to Sync thinking there are conflicts when multiple clients are running, but I could be wrong.
Anyway, that aside I assume your goal is to keep the MySQL and MSSQL databases in Sync? If this is the case then why not run a server-side process in front of the MySQL database that becomes the Sync participant. If you've got alread .Net on the server-side you could even write it in C#, which is bound to ease the interop issues.
If you are set on the client being the Sync participant then take a look at Jakarta Commons, which I think has the code you're need to turn you client into a simple web-server that'll be needed for it to act as a web-service or RSS feed.