This is indeed supported. Best thing to do is
1. Enable logging on both machines
2. Create a new profile on both machines to force an initial sync.
3. After initial sync, verify home, work and server show the same data
4. Leave logging enabled. When you run into this again, submit the logs to support.
If you're running 4.5.x and not 5.0.x, you may encounter this issue because of this bug:
Bug 6530 - cannot drag items from one store to another -- do not appear on server