Yes, and repeated practice at performing _in front of an audience_ will gradually reduce that anxiety for most people. Getting to that state where you can be up in front of a lot of people and just enjoying yourself making music is a wonderful feeling, and for most of us it takes a lot of hard work over many years.

In my personal experience, both with musical performance and public speaking, the #1 thing that makes a difference in terms of how nervous I am during the performance is how well I know the material. The more I can "shut off my brain" and let rote memory handle the basics (correctness), the more room I have to take it further with nuance, dramatic arc, etc.