Sort of. Assuming we are talking about the type of punch driven by a flywheel that can exert an order of magnitude more force than it is designed for if set up incorrectly, then yes, a hydraulic press would just stop itself.
Granted, you can still use a die that would be obliterated by full tonnage of the press, but hydraulics lend themselves to adjustable tonnage pretty well. Not that anybody uses it. Our Adira press brake stayed cranked at 70 tons unless we were doing something premiumly sketchy. Though being able to accurately adjust pressure without having to have something pinched in the machine would go a long way towards making that safety feature a convenience instead of a nuisance.
(Of topic story, but our Adira brake has a high and low flow pump. We adjusted the speed transition switch so it would stay at rapid travel for the full stroke. The pressure relief valve was actually pretty solid down to 2 tons, so we pressed in a batch of 800 bearing races with it. The guy taking the bearings out of the individual bags couldn't keep up with the guy doing the pressing).