Merging Events in Mixpanel Using Email with Calendly Integration

Is there a way to merge events into a user, where the only thing they have in common is an email property on the event? Unfortunately we're using Calendly, which only has the ability to pass an email to a user. We use Mixpanel with original Merge, via Rudderstack as the event CDP. I understand there is an $alias call - but I'm not super cler on how this interacts with Rudderstack?