They can indeed, it's the owners site so yes they can do whatever they can with your bitcoins. I don't think gambling sites would change anything though, it does more harm to them. If you win big try to withdraw as soon as you can.
Yes withdrawing your profits often must be a most recommended with respect to gambling to keep your funds safer from yourselves as well as from gambling houses.
As long as money is not in our control, the site owners can do anything with it. Out of greedy many gamblers simply raise their betting amount and end in wiping out of their profits.