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I agree with all the advices to get faster lens rather than flash - I have photographed some gymnastics, and most of the time, flash is NOT allowed. This has to do with the safety of the athletes (the ones you're photographing as well as those you're not). Flash can be distracting and at times, harmful to athlete's vision if looked at directly. It's definitely a safety issue.
That said, you'd be surprised how much 2 stops can help (going from 5.6 to 2.8). Of course, more is better here, but then you struggle with focus speed and accuracy and thin DOF.
With the D7000, I wouldn't hesitate to use a 70-200/2.8 VR or equivalent. You may end up using higher ISO than you'd like to.. but at least the D7000 is good at keeping IQ reasonable. (much more so than film ever did!)
A lot of people still aren't satisfied with high ISO IQ in current offerings. Of course, anything can always be "better". But if you consider the quality we used to get from print film (think of those grainy 1600 films!), or even compare to a D200, we've come a VERY long way, and I don't think that 10 years ago, most people could have anticipated our current high ISO performance being actual reality this soon.
Sometimes, it's not all about the IQ, but actually capturing the moment! Especially to athletes, catching it just right, and seeing themselves in all the glory in a well made photo trumps our standard judgment of IQ any day. Heck, it could be a grainy black and white picture for all they care, as long as the capture was a good one!