Absolutely. Your progress and high scores will be saved between sessions.
awesome, cause that makes a big difference to me! a lot of arcade-ish games didn't do this, had no save feature and/or highscores would be erased when you turned the game off. Made it harder for me to enjoy them.
I am interested in the physical copy of this, I think it seems cool, but only problem is I don't have a Gameboy.