In a recent blog post, Chicago Booth's Rose Martinelli opened the door to third round applicants. While Ms. Martinelli conceded that the third round is more challenging than the first two rounds, (The truth is that R3 can be a bit more competitive simply because the majority of applications and acceptances will occur in Rounds One and Two.) she logically explained that the school has a third round for a reason and emphasized that a good portion of our class will be admitted from R3 as well as a good number being placed on (the) summer waitlist.  

Providing some clues with respect to competing in the third round, Ms. Martinelli suggested that you might explain why you are applying a bit later and not be afraid to be honest. She allayed the concerns of internationals, explaining that visas can still be processed in time and cautioned against rushing and throwing in a haphazard last ditch application.

If you are contemplating an application, you have nothing to lose... (but your time and application fee).