Hm, I don't see how this could get you flagged as a cheater.
I have Chessbase 10 open 99% of the time I'm logged in here. How else would I be able to use my database for cc games or my cbh and pgn opening books?
While I don't use them in live games, of course, I certainly don't bother to close Chessbase just because I play a couple of blitz games or something.
Never had a problem because of that.
Sometimes when I close out of Chessbase it gives a message with a red circle and x saying restart (recommended)? It doesn't of course, but when I run the task manager it's still running in the background!
I say this because it not only eats up valuable RAM but could get you unfairly flagged as a cheater simply for running (though not open in a window is technically running). It didn't happen to me personally, but always check task manager before playing a game!