Sorry to bring up an old thread. Now that I've graduated and gone through the recruiting process, I wanted to answer my own question for others who may be wondering the same.
I don't think a 1 year (or 10 month) program puts you at a disadvantage for consulting recruiting. You just need to make sure you spend enough time prepping for the interview. Kids at INSEAD (as well as Kellogg 1 year program) regularly get into MBB and beyond.
Consulting companies want smart people who can crush the case interview. It doesn't matter if you were a teacher, a marketer, an entrepreneur, or a profession athlete. As long as you show them you are smart (through grades/interview) and cool (through networking), you can get an interview and, if you interview well, get an offer. Interviews don't test anything you can't learn in a book like Case in Point.
Note that this is specific to consulting recruiting. Industry recruiting (tech, health care, education, energy, etc.) often care about previous work experience and having a summer internship really helps make that jump.