I applied May 21 (literally the deadline), had all my letters sent by May 25, got an email June 2 saying my application was under review, and another email June 11 saying I was accepted (I didn't see it earlier since I was away this weekend). So looks like about 9 days of review for me.
That being said, I had a June 5 deadline to accept an offer at another SMP that I applied to around the same time, so I went ahead and took that rather than wait for Georgetown. Bird in the hand is better than two in the bush. Haven't got the email that would let me decline the offer yet, but once I do, I'll be sure to fill it out right away and get someone off the waitlist ASAP.
I actually applied to Georgetown's SMP last year and got rejected then, so here are my stats:
Spring 2016 (rejected): ORM, Majored in Neuroscience at a top private school; strong leadership-based ECs; about 600 hours nonclinical and clinical work experience plus some shadowing; minimal research experience; upward GPA trends in last half of undergraduate leading to a 3.3cGPA, 3.1sGPA; 509 MCAT (129/124/127/129), I think CARS plus low GPA killed me
Spring 2017 (accepted): Spent gap year working at an urgent care and getting tons of patient experience (~1200 hours); took enough post-bac science classes at a state university to raise my GPA to a 3.4cGPA, 3.2sGPA; retook MCAT and got a 521 (131/129/129/132).