It is indeed possible.
In HS I ran an 18:53 on 500 miles of training (February 2001-August 2001). Peaked 9/15/01 due to 9/11 and a few other things. I actually peaked early and was not able to make it out of district b/c I started training too early.
Got out of running for 7 years.
Started training for Kent State Bowman Cup 5k in October 2008. Started July 2008 with 2-mile test @ about 19:20 (9:40 pace). 5k was around 29-ish. Did about 25-35 mpw, with longest run being 13.3-miler in mid-Sept. (9/15/08) as a LSD. Only 2-3 weeks of speed work (4 1200 @ 3:43-3:50, with 2 mins. rest in between). Race was mid-October. Ran 18:33. Didn't run enough distance but still dropped 11 minutes or so.
It can be done even on a slightly undertrained body. If you have long legs you're good to go. I'm only 5'2'' and still improved fast in a short period of time and with a long layoff. I decided to quit running, not because I got hurt, but because it took up a lot of free time and walking was more practical at that point in my life.
Point is--if you get the LSD in w/o getting hurt, don't do speedwork until you have a base, and taper properly you'll run faster than you think on race day.