Will Automations still run if a user is removed from permissioned groups?

We have a notification system that a user set-up on our platform. If we remove them from heavily-permissioned groups on the platform, will their automation still run with the same expectations?

If using automate’s “notification effect”, then notifications are sent on behalf of each recipient, so the automation will still run

If using a “logic effect” or an “action effect”, then the automation will not run as those effects will be run on behalf of the owner