Yes, you can in San Andreas. I'm not sure about Liberty City or Vice City, though. In Vice City, I stole a boat and was almost to the other island before the cops showed up and blew me out of the water. If the cops hadn't showed up, I would have gotten onto the other island before it was "officially" unlocked. As for San Andreas, It's easy to get to the other island before it's unlocked. Go to Unity Station or Market Station and wait for a train. Instead of boarding a passenger car as a paying passenger, walk up to the locomotive and hijack it just like you would a car. Back the train all the way to the rural area to get a good running start. It takes a l-o-n-g time to get a train up to the ridiculous speed you need to crash through the barrier. Now floor it! If the train starts shaking (you'll feel the controller vibrate on the Xbox or Playstation), ease up on the gas or the train will derail and stop. Also, slow down slightly before that sharp curve just before Unity Station or you'll cause a train wreck with train cars scattered across several blocks (fun to do, but not now). Keep the gas floored from now on and you'll blow through Unity Station and then Market Station. If you have enough speed, your momentum will carry you through the barrier on the RR bridge and you'll be across the river. But now, you have a 5-star wanted level. so there's not much you can do but stay in the train and keep going. You'll be chashed by police helicopters and SWAT units, but there's nothing they can do to stop a train! You'll eventually make a complete circuit and arrive back in San Andras (Provided you keep your speed up so you can crash through more barriers between other locked islands). At this point, you options are to just keep going in circles forever, stop the train and surrender, or cause a train wreck. Have fun!

Ooh, I know! I discovered this while playing the trucking mission 5.In this mission you are trucking stuff to San Fierro.If you complete this mission, you will step out of the truck in San Fierro, without stars! I believe it also works in the last trucking mission when you go to Las Venturas. Except then you will have a four star level until you complete the mission.