There's no way to seal them, so yes, if you have the bag full to bursting, its going to leak a bit.
In general they do very well with keeping things dry. I took one out for an hour and a half during a heavy downpour that soaked me to the bone (although almost no wind so at least the rain was straight down) and it kept my camera mostly dry (I think most of the water that did get in was from opening it up to get the camera out). So they do very well but if you're skipping through a typhoon, there's going to be some water in the bag.