You should start your applications when the cycle opens and it will take a month to get transcripts in, things verified, rec letters, etc. Your application would be complete in ~June but waiting on MCAT and you'd have potentially secondaries coming in. If you took the MCAT in mid-June it would be released ~mid-July. That would be early in the cycle still and you update your application and it notifies schools of your MCAT. It's a risk doing it that way, because if you bomb the MCAT you really won't have time to retake as schools you applied to may eliminate you, but with 4 months of studying just DON'T.
Best of Luck