Hi hheeyyy and welcome to the Mattermost forums!
The recipient will (by using the official clients) not be able to see the edit history. The edit history is stored in the database, though, and a custom client could have access to the edit history, if implemented accordingly. There are API calls to get information about deleted posts and an edit is basically just a re-created post with the old one being deleted.
The recipient will not receive a notification using the default clients, but that’s also up to the client implementation. There will be a visual indication to show that the message has been edited.