How important are summer intensives when actually auditioning for ballet companies?

What is more important is your full time training in a professional ballet school. In many cases you won't get to audition if your training has not been on a professional level in a professional school. Many Intensives are just money makers but they are also stepping stones to getting into better training and eventually a ballet company. As year round training on a professional level is essential for a ballet career many companies pull from their SI programs for dancers to attend their full time schools and pull dancers from their full time schools to be in their companies. More people get into professional ballet companies by being first in their SI program and then asked to train full time with their affiliate feeder school. So they are important more as a way into better or continuous year round training. Going to SAB SI means little if you aren't asked to study full time with them at the end of the SI.

EDIT: As you are already 16 you should be apprenticing with a professional ballet company at your age. That means company ready and not just taking 8 hours of ballet classes a week and asking about SI programs. My guess is you are far too undertrained for your age to audition for a professional ballet company if they would even let you audition. I am sorry. Not what you wanted to hear but if you haven't had at least 2 solid years of intense full time pas de deux training at your age you are not close to being ready for a professional ballet company audition. Many companies don't even offer open auditions but pull directly from their or other top school full time training programs.