Hi Suki, sorry for the delay in replying. The last few days have been manic nd I've hardly had time to log on in between the extended sleeping, lol.
In answer to your question, it shouldn't be a problem, though if the games manager requires certain services (which I doubt it will) that are automatically shut down by Game Booster then there could be a problem.
However, that said, you can taylor Game Booster to your own requirements. What I mean by that is; you can toggle on or off all of the services which by default the application closes down. So even if BFG's manager did require a service, you can make sure that its not turned off when you use Game Booster.
I hope this answers your question.