That depends on the application deadlines for the schools you're applying to. They need to receive a completed application, including your official GMAT scores, before they will review your app. It takes about 2-3 weeks for your official score report to be sent to the schools, so if the deadline for the round you're applying in is mid-late January or after, you're fine. If the deadline for that round is before then and your scores haven't arrived yet, they'll just bump you to the next round. Not usually a big deal unless you're then put into the final round, which tends to have lower acceptance rates.
I wouldn't rush the application if you have time between your GMAT and the deadline to hone it. You should be spending much of the next month preparing for the GMAT, and then once that's done, finalize the rest of your app. If you haven't already done your essays, take as much time with them as you can. They're extremely important and should NOT be rushed.
Good luck!