CiviHosting and MySQL 5.7
IMO the only way to answer this with confidence is empirically: request a trial upgrade in the proposed new hosting environment (or equivalent), and test whether the system upgrades then functions as expected. Most effectively done when you have some tests that you can run on your newly upgraded site to ensure things function.

Fuzion host on MySQL 5.5 and 5.6, so I can't speak to what you should expect on MySQL 5.7. (This is not because we don't approve of 5.7, we just have had no reason as of today to move there.) 

You might also see variation between Percona / MariaDB / MySQL, or between various OS or distribution packages ... Your best bet is to try it and see! Just not in production ;)