Yes, that is absolutely true. People get hired because people hire them. So if you're seen doing gigs, you'll be building up the idea that you are available for hire.
One thing you need to learn very quickly, though, is there's a big difference between working for "free" and working for "nothing."
You don't want your reputation to be that you work for nothing. You don't really want it to be that you work for free, either, but when you're starting out you're not going to get good fees (unless you're some business savant).
Try to get your name and information put on the advertising for events you work. Get a poster made, maybe. Definitely have business cards. If you're not a designer, though, keep your business card super simple. Better to have a classy one that just has your name, a title, and your number than some garish cartoony attempt to do the graphics yourself.
Also - and this is something I see constantly - make sure your email address isn't childish. It should be some form of your name, and ideally dedicated to the business stuff. Preferably you'll get your own site, but gmail is fine, too. But I can't tell you how many people try to say they're a professional entertainer and then say their email is something like
LordSniperSnout@hotmail.com. Lose all credibility right there.