In the absolute, I guess the best would be to take advantage of some update to the game (bug fixing/content addition/whatever stuff of the like) and as you would export it with the business version it would be all good.
With my speed of development this might be far away I have created some small games for personal learning but it takes a while to have confidence to publish something publicly.
No, you don't need to republish your game.
Thanks for the info