Currently I don't think it does, and because the creation of stagings is only triggered, if re-enabling during a period of low activity (e.g. late evening because you just remembered that you should check if https://www.githubstatus.com/incidents/cqb5hcy0gx18 was resolved) it's then necessary to trigger the cron manually.
Also check if restoring staging on a branch triggers the staging cron, for the same reason.