There might be a brief downtime while the domain propagates to the new IP, usually not much noticeable, the premium hosting is on separate servers.
Putting the site in "maitenance mode" is recommended if possible, especially if you have users posting to your site in any way, to avoid discrepency with data where the users post to the version on the free hosting server after the account is prepared for migration, as changes after that will not automatically updated on the premium server.