It's very easy. lists.sr.ht, for example, supports importing and exporting mailing list archives as mbox files (a well-known format for email storage).
I know Drew is working on a few email things for the `todo` section of the site. Opening tickets, and responding via email.
> Can I participate in tickets on Sourcehut without creating an account?
Depends. I set up most of my public ones to allow anonymous users to contribute, but it's up to the owner to decide whether they want that or not.