It occurred to me that cycling primarily involves heart, lungs, and legs. You train all of them simultaneously, so they'll naturally have balanced performance. If you selectively impair one of the three, it will become a bottleneck. However, it seems to me that the lungs have the easiest job (e.g. cycling is easier than tasks like inflating balloons), so it should be possible to recover almost all the lost performance by training with the respirator on, bringing the lungs back into balance with the heart and legs.