Yes, your existing files can keep right on being used when you get your license. The data files themselves are unaffected by the application's license. You can even change from FMPro to FMProAdvanced.
I believe you may not even need a new installation, but might be allowed to simply enter your new product registration code in the installed copy to change its status. (This may not work with a VLA license.)
jeoihcd may have put FMP on trial,
Don't worry about it. The DB file is the same, fully functional, and usable with FieMaker Pro/Advanced/Server/Trial.