From the customers that I have that use Genesys, I do know that when they reboot the Genesys server, a reboot of the Symposium is required to get them to sync up again.
As an FYI for others, the Genesys is only using the Symposium for the MLSM link. Sets are acquired, but agents don't actually log into the Symposium. Calls come in on an agent's DN key, not on the In-Calls key. This is how I have seen it work in two different environments.