Does the flywheel have to be removed to drop the transmission?

no, it doesnt have to come off. Actually the trans has to be out of the way to take it off. Did he do the rear main seal? That would be the only reason

Why wouldn't it start. Binding. Did the starter turn the engine over or just stop dead once engaged?? As per your question, they would be no point to remove it. once you have enough clearance to get at the bolts the tranny would drop out! I'm thinking that the torque converter slid out on the shaft disengaging from the pump. Then when the tranny was installed the torque converter bent the flywheel towards the motor from the pressure from bolting it up. This in turn caused enough binding to not allow the car to start. I always spin the TC while bolting up transmissions to ensure it doesn't bind. Just hope the pump was not damaged in the tranny.

Sorry Andrew you slid in there while I was typing. Yah seal maybe.

Get the GM tech to inspect the TC, flexplate and pump.

as everyone said it does not come off but you must describe what the car is doing when you try to start it to determine the cause .does the engine turn over .does the starter engage .does the starter spin without the motor turning .does nothing at all happen no noise .is the starter grinding all these things can be the problem and thus many different fixes