Probably possible, upper body only and only while seated or laying down. Assuming precise 2.2 or non weight bearing. Weight bearing you still won’t want to do squats etc at risk of bending the nail. Regardless I wouldn’t do any standing exercises while lengthening. Nails breaking is basically the biggest catastrophic failure, you will have to pay for a new nail and surgery, which will REALLY fk you up.
That said you will be burning a lot of everything: fat, muscle, etc while you lengthen as your body spends a lot of calories healing. Your body will be constantly healing. Working out hard while you also do that is probably a bad idea. You do not need the extra stress or muscle building in the upper body while your lower body is under the biggest possible stress there is. But a light workout just to keep the motions up for a few months… still not great but probably fine.