You can use it, but it'd be a lot easier to just provision one inside of Nanobox. You don't need a second Nanobox. It'll provision a single VM, then build whatever components/containers are in your boxfile.yml.
That would provision a php code container and a mysql container inside the Nanobox VM
you'd be able to connect to the mysql database from the php container
However, to use your local mysql db, you'd have to expose it to the public network in order for anything running inside of nanobox to communicate with it.