This is not only possible this is also the default. You can turn it off by setting the following config option to
I believe when using the local job runner running jobs will be cancelled.
Jobs that have not yet run (e.g. queued or gray) will still be started after the server restarts as long as track_jobs_in_database is set as Martin said.
For running jobs to survive a restart you need to use a separate DRM such as SLURM.