Question: I am planning on applying early decision to my first-choice college. I will be notified of my status by December 31st. My second-choice college has an early decision deadline of January 1st. If I do not get accepted by my first-choice college, would it be appropriate for me to apply early decision to my second-choice college?
Yes, this is a "strategy" that students use successfully all the time. The only thing that may be tough for you is this: if you are deferred by your first-choice school and not denied outright in December, you may always wonder if you should have waited for the regular-decision round.
However, if your #2 choice is a close second and you want to get the admission process out of the way as soon as possible (can't blame you there!), you will certainly boost your chances of acceptance to College #2 by applying E.D., and thus this seems like a reasonable plan. By the way, there are some colleges that share lists of admitted early applicants, but if you don't get into your first-choice college, then your second-choice school should have no way of knowing that you applied elsewhere already.