There is no function in the current implementation of 3CX Phone System that will send information to a Syslog Server.
I can't see though how accessing the DB would accomplish that. Just an FYI, all logs are stored in C:\ProgramData\3CX\<InstanceX>\Data\Logs\ and if you want to have live updating, you could use the 3CX Call Control API to make your own projects that will have some listeners for various events and update a Syslog Server. http://www.3cx.com/blog/docs/call-control-api/