How long does it take for powershell to restore a SQL Backup?
You are setting the restore to not recover your database.

$res.NoRecovery = $TRUE

Remove this line or set this value to $FALSE and the database will restore as you expect. 

This setting is useful when restoring log backups. This includes when you restore the tail of the log. Books Online has more info here

As for the duration of a RESTORE it depends on your storage and the size of your database. With that said, 80MB shouldn't take very long at all.