It should not core-dump (read: hard crash, something has gone terribly wrong), at best you should get a configuration error and errors like that.
You can see the logs of any systemd service/unit with this: journalctl -u <name of sevice> so in this case journalctl -u jellyfin (Tip: add -f to follow the output of a running service - useful for monitoring).
Note that some programs log to their own files (and not to stdout) so if the above command comes out empty you should look into /var/log/ directory.