ESXi will basically just pull the plug. That is very bad for MySQL.
You would want to either shut it down through the Web interface under Administration and Shutdown or access the CLI and just type shutdown. That way the OS will shut everything down correctly.
One suggestions I would make is to make a new image of the appliance or clone a current one and test the shut down while looking at the console. If you see a bunch of items shutting down gracefully you know it will work.
If you have us running on an actual appliance, the power button on the server will tell Linux to gracefully shut down, so if ESXi can duplicat ethat same command it should work.