With typical baseball, yes this is allowed, but you mentioned a specific governing body so I looked it up.
12.03 Runners shall not advance when the pitcher is on the pitching rubber with the ball in his possession and the catcher is in position to receive a pitch. On a base on balls, the batter may attempt to steal second prior to the pitcher and catcher coming set at his own risk, but if a runner is on third, he may not advance home even if the defense attempts to throw the runner out at second base.
This is usually only an issue at the younger ages. We taught our kids to run full speed to first even on ball four. This way if the catcher was taking his time getting the ball back to the pitcher, or the pitcher was sulking his way back to the mound, or if no one was watching the runner and covering second; you could send the runner to second. You'll notice at the lower ages some teams are prepared for it. The catcher will get the ball back to the pitcher quickly and the pitcher will almost sprint back to the rubber. Some teams will also keep the pitcher on the rubber and have the catcher throw it back to the pitcher as he's standing on the rubber. But the answer is yes, you can advance past first on a walk.