Can an automatic transmission shift while the torque converter is locked up?

 

Yes. Not always the best idea, but it can do so.

 

With the converter locked, the engine rpm has to drop rapidly at the shift. The engine (with converter mass) has a lot of momentum and since it can not drop instantaneously, something has "to give":
1. With luck, only the frictions in the trans will slip and wear out prematurely.
2. With less luck, a yoke, driveshaft, axle or trans part will break catastrophically.

 

Or wheel spin if on street tires. But I still wouldn't do it.