According to the GMAC, the GMAT score is the best predictive metric on how well a student will perform in the first year of business school. It is more accurate than undergraduate GPA or work experience.
I think the reason for the strong predictive quality of the GMAT, is that for the vast majority of people, a high GMAT score takes a combination of brain power, discipline, and hard work - which will definitely come in handy at B School. Additionally, the GMAT is usually the most recent indicator of such attributes. So for instance, a high undergraduate performer may have lost some academic drive since college and therefore does poorly on the GMAT. If you assume that the most recent behavioral patterns is the best predictive measure of the near future, this student likely won't do so well in B-School. This is likely why the GMAC only reports the correlation to first year performance - as time progresses behavior changes, so the GMAT's predictive capabilities diminish. Furhthermore, unlike GPA's and work experience which are subject to so many varying factors, such as difficulty of courses, difficulty of school, how much your teacher or boss likes you etc, the GMAT is an extremely level playing field. So it is no surprise that the GMAT is a strong academic predictor.
That said, I wouldn't assume you would or would not do well in B School based on your GMAT score, whether aided by a tutor or not. If you know you are smart and an extremely hard worker and just have a hard time with standardized tests in general or the GMAT in particular, you are probably quite likely to do well in B School. On the flip-side, if you can walk into a test center and score a 790 with your eyes closed (see
story-that-nobody-wants-to-hear-107050.html#p846321), that does not mean you will do well in business school - particularly in the classes that rely more on hard work and discipline than raw brain power.
So in short, yes the skills you learn studying for the GMAT will likely help in B School, but more importantly, it is the ability to combine your intellect with hard work to do well on the GMAT that should indicate how well you are likely to perform in B School