If you do a proper barrel roll, you maintain 1G at all times andf don't harm the aircraft or disrupt it's systems. But if you screw up...there are several known cases of commuter pilots rolling (empty) turboprop airliners on ferry flights. The ones I am aware resulted in sever structural damage (and even worse career damage), but maybe that's because regional pilot skill was lacking. I bet Sully could have pulled it off!
I think that a large transport category might be recoverable from a developed spin using differential power...turbofans make a whole lot of thrust. But the airplane could very well tear itself apart before you got the chance to recover. As someone mentioned: centrifugal force.
The Lockheed Electra can definitely recover from a spin...once. After that it's off to the beer can factory (the navy demonstrated this in 2008).