Let us refer to "nerves" or nervousness as anxiety, which is a more comprehensive term for what we are discussing. In my understanding a direct link between anxiety and physical exercise would be this: if you are physically active the amount of anxiety is lessened, perhaps in proportion to the amount of each.

Has such link been established by medical science? The answer is yes, with an overwhelming amount of evidence. Little of which I have referenced below.

An aritcle was published in the Research Digest of the Arizon State University on this topic. It is an unbias meta-analyses of close to 200 studies with over a thousand subjects. You can read the full article at this link
http://www.fitness.gov/mentalhealth.htm

But I also listed several quotes after reading it myself:

'Landers and Petruzzello (1994) examined the results of 27 narrative reviews that had been conducted between 1960 and 1991 and found that in 81% of them the authors had concluded that physical activity/fitness was related to anxiety reduction following exercise and there was little or no conflicting data presented in these reviews. For the other 19%, the authors had concluded that most of the findings were supportive of exercise being related to a reduction in anxiety, but there were some divergent results. None of these narrative reviews concluded that there was no relationship.'

'All six of these meta-analyses found that across all studies examined, exercise was significantly related to a reduction in anxiety.'

and...

'The research literature suggests that for many variables there is now ample evidence that a definite relationship exists between exercise and improved mental health. This is particularly evident in the case of a reduction of anxiety and depression. For these topics, there is now considerable evidence derived from over hundreds of studies with thousands of subjects to support the claim that “exercise is related to a relief in symptoms of depression and anxiety.”'

In addition to the comprehencive review above, I listed some credible sources that support the same idea:

http://www.mayoclinic.com/health/depression-and-exercise/MH00043
http://www.sciencedaily.com/releases/2003/07/030715091511.htm
http://www.mclean.harvard.edu/news/press/current.php?id=86
http://health.msn.com/centers/depression/articlepage.aspx?cp-documentid=100096414

Ren, on a side note though, I see you not referencing to any negative side effects of your stage fright. I didn't hear that you skipped a show, or threw up on your audience. Perhaps due to your consistant exericese they are little present if not at all, and the stage fright you mention is nothing more than an additional energy you're getting for a challenge of another performance.