I don't think so, no.

A possible solution would be to attach a database trigger to the relevant table(s), sending a notification to FME Server when anything changes. There are many possibilities for the trigger mechanism: https://docs.safe.com/fme/html/FME_Server_Documentation/WebUI/Automations-General/Automations-Triggers.htm

There is a Directory Watcher in FMEServer. If your SQL database log file is put in a directory, and it is updated, then Directory Watcher could detect the change and do something.