That is highly unlikely.
Remember the plane in Hawaii a few years ago that lost a large piece of the fusilage and the pilot managed to fly it and land it with the only fatality being someone who was sucked out through the gaping hole.
Bullet holes would cause decompression, but not likely cause catastrophic failure.
A greater danger would be if a bullet punctured a hydraulic line causing loss of control.
Yes, the 737 "convertible."