So, almost everyone who has experience applying to med schools this cycle took the MCAT in 2006, which means that "late" meant August, scores were verified in October, and it did indeed hold up applications. How much this actually hurts applicants is unknown, though the common belief is that it's detrimental. (We should actually do a scientific study of this sometime using SDN data).
You, however, have the advantage of the computerized MCAT which is available significantly more often then it was in previous years. Also, it only takes about 30 days for you to get your score back.
So, say you submitted your primary on June 1, then took the June 15 MCAT. Your application would probably be verified in mid-late June, you would start working on your secondaries, and your MCAT scores would be released by the July 15. This would probably not hurt you at all. Mid July is still very early. That being said, who knows what the application dynamic will look like this year - more people might take the test "early" (ie, before June) because there are more opportunities to do it.
Basically, you have to do what's best for you. I'm guessing you want to take the MCAT after you submit your primary because you want the extra time to study. If not, take it now. The most important thing is that you do well on the MCAT, and do well in classes, so if you can't do both without taking the test until the summer, it's not the end of the world, just be smart about it. Taking the MCAT in July will still allow you to get your scores back by August, so if your secondary is completed in August, that's still pretty good.
Try to maximize your score and the promptness of your application to the best of your ability. Some secondaries require no essay (WashU, Penn, Harvard), and some allow you to work on the essay before your AMCAS is verified, as someone already said (Columbia), so that will save you time. You should check for the schools you are interested in. It is important to allow your self ample time to do a good job on your secondaries. Schools actually do look closely at these essays as well as your personal statement, and it behoves you to write good essays. Aim to be done as early as possible, but realistically before September.
Sorry this was long. Hope this helps! Good luck!