A word of caution: if your single user file gets corrupted, that corrupt copy may be pushed to all of your devices effectively eliminating any useable copy. I spent a little time creating a backup script for my single user files that on closing makes a time stamped backup copy of the file: 'file 201108120433.fp7', for instance. Filemaker Server makes fantastic backups and once it mastered the technique of making a backup with strangling the network, I did a unique hourly backup for each day of the week. That leads to another problem... :)
I don't think this would work as you imagine it might.
For FMGo on any device, the app does not run the database file that is in your SugarSync folder. It creates a copy of that file, and opens it within the FMGo app. Now you have two files: the one available in SugarSync, and a newer one in the FMGo app. There is no way to get that file back on to SugarSync that I know of. So, you have to connect to iTunes and pull that updated file off manually and manually replace your SugarSync copy. If you are working from multiple devices, you will end up with multiple files, all based on the SugarSync version, but all containing on the updates from that device. You'll have to find a way to transfer new/updated records back into the main database.
Dropbox works the same way, as do similar services, I imagine.
However, as long as you have a wireless connection and network access to the file running on FMPro, you can open the file on your desktop via the network (including internet), so there is only one copy that is updated by all devices.