I would not expect it to work — in nearly all cases, a backup made on a newer version of iOS cannot be restored to a device running an older version (the restore would fail with an error if you tried, whether the backup was on iCloud or local).
If you made a local backup prior to installing the 18.1 beta, you would need to use that instead. If not, you may be out of luck for any data that cannot be synced back to the device via iCloud or similar services.
[Addendum: You could also restore from an iCloud backup if, and only if, the backup was made before the device was upgraded to the 18.1 beta and the iCloud backup feature was then turned off to prevent backups from that device while running 18.1 betas; as soon as a new backup is made on 18.1, you can no longer use those iCloud backups to restore the device running 18.0 or earlier.]