Yes.

Everyone (well, males) starts off at Cat 5, juniors included. So as long as the race does not have any age restrictions (i.e.: Master's 35+ or 55+ or whatever) or gender restrictions, you're good to go. You just have to race your category and adhere to the Junior gear rollout limitation.

If you're planning on racing at least 6 times or more, it's worth it to get an annual license. Otherwise, pay the unlicensed rider fee (usually $10).