You can certainly collect things for your tank from the beach if legal. Just make sure you know what you're adding. You're far more likely to introduce diseases from the closed, overcrowded systems of the wholesalers and retailers out there. Most fish and inverts we add to our tanks are collected from the "beach".
Many people also run native tanks, where all the livestock is collected from the beach. While you're there get some "bugs" out of the water and feed your fish.
Welcome to R2R. As said above, you need to check with your local ordinances to see what is legal and what is not. But if you do, QT them before going in your display.
I actually have a friend that had a small tank of gulf creatures (all legal of course) and it was quite interesting.