Privatemsg through a Multi Site configuration? Is it possible to do such a thing for users in site 1 to message users in site 2 and visa versa? Using the Privatemsg module?
Multi-site is just a way to share code. Different sites are completely separated and know nothing of each other*.

There might be ways to theoretically do this using special recipient types, it would have to use services (or raw SQL queries) to another drupal installation, multi-site or not. And it wouldn't be easy to implement and likely also be very slow.

*With the exception of shared tables, but if you'd share your users, you wouldn't have different users in the first place.