Yes, you can hunt with a short barreled, cylinder bore barrel. It can even be an advantage for early season, thick bush hunting.
The effective range will vary depending on the shells used - primarily due to the shot cup being more effective at keeping the shot string bunched up with some loads.
Chances are that your effective range will be no more than 25 yards, but there's no way to be certain unless you pattern both barrels with the shells that will be used.
If the barrels were cut, there's a high likelihood that the regulation will be off, too (see the other thread on chopped SXS barrels in the "shotgun" forum today).