As Mushtaq2k15 mentions above, SEE uses a MS SQL DB, which is called SEEMSDb by default (though it can be changed). There is no builtin option to output information to syslog in SEE.
What kind of events are you after? The dbo.Computers table contains records of the current/last state of managed clients, while the dbo.GEMSClientEvents table holds events uploaded by client when they check in. Not to mention a whole load of SQL Views on the data to boot. I'd recommen you have a look through the various options, as I was unabel to find a SEE DB Schema reference article.
If you're focussed purely on client communications, you could always enable IIS logging, these are simple text files and easily ingestible by SIEM solutions.