YES IT MATTERS! You should submit your AMCAS and requested LORs long before your scores come out. That way, as soon as your scores are released, your application will be complete.
A lot of schools allow you to access their secondaries before your AMCAS is even verified. The only reason you may not want to begin applying is if it's contingent upon your August scores and you don't want to waste the money.
I took my MCATs last aug, however i will be taking them again this august. Does it matter if i apply now or a few weeks before the release of the aug MCATs?