It does happen, but it wasn't easy.
I took the MCAT back in August without having my bio or orgo pre-reqs done yet. I had to submit my AMCAS before I got the results back in October (extremely nerve wracking, but I scored a 34). My original undergrad GPA was 3.98 in engineering, and my wife works in the medical field (it makes an impression on interviewers when you've been living medicine on more than a volunteer or scrub job basis, but I did have those things as well).
I got an interview with my first choice state school and was accepted with the contingency that I complete the pre-reqs before school starts in August (will finish in the spring).
I'm probably definitely the major exception to the rule, but it can be done.