The reference guide says:
Defines which storage service module will be used. The storage service module takes care of storing the actual files asssociated with 'System.FileDocument' objects, such as uploaded files. Possible values are currently 'com.mendix.storage.localfilesystem' and 'com.mendix.storage.s3'.
My guess is that it just switches the usage and does not transfer files for you. But if you want to make sure, just contact Mendix support. And please let us know here. ;-)
As you probably guessed, no, changing the storage settings will not migrate the data. You will need to do that yourself.