Can I hook up pressurized hydrogen to a gas piston engine and have it work as is?

This is possible, and common, for the cases of both propane and natural gas. The pressurized tank is connected to a pressure regulator that works just like a scuba regulator, which sits where the carburetor was on the engine. When the piston goes down and creates a suction in the intake, the regulator opens up a bit and injects some gas into the intake manifold, then shuts until the next suction phase.

This setup requires some adjustments to guarantee the correct gas/air mixture for best performance, but that is not hard to do, and propane/natural gas conversion kits can be bought commercially right now.

Hydrogen conversions are possible in principle but not yet available in the market because there is no cheap source of H2, no distribution infrastructure in place for it, and no solution yet to the problem of safe, light, and inexpensive extrahigh-pressure H2 storage tanks for mobile use.