The Open Beta is 2.5.2, it is designed for early access of modules for public testing. Version 2.5 is the stable version and will get PG in the near future - historically it has been within 2 weeks. (that is not a guarantee just the "norm")
Once a module is activated on your computer, with your account, it doesn't need to be activated again with different versions of DCS. The short answer is, no, you will not need to use another activation when it is available on 2.5.x stable.