This is an interesting thought. AFAIK the main pathway for building things is HIF 1 alpha. There are thoughts that it also has broader effects potentially through the transfer of mitochondria and it definitely has some effects outside the cell in which it starts off. It would be an interesting test. I would not, however, think the non exercised arm (remembering that any movement is a form of exercise) would become that much stronger.

The inactive limb gains about 40% of the strength gains for the trained one:

training programs organized into multiple sets (3-5 sets of 8-15 repetitions with rest times of 1-2 minutes) obtained strength improvements in the opposite limb up to 39.2 ± 2 7.8% of those achieved in the trained hemisphere.

https://www.jssm.org/hf.php?id=jssm-16-180.xml

In this study, those that trained their mobile arm only lost 2% of the muscle in the immobile arm, compared to 28% for the group that didn’t exercise:

"This group also had just two per cent muscle wastage in their immobilised arm, compared with those who did no exercise who had a 28 per cent loss of muscle.

Transfer of mitochondria from muscles to other parts of the body, like the organs and the brain seems very interesting to me. That would justify doing a lot of zone 2 exercise (maximizing creation of new/better mitochondria by exercising at 2 mmol lactate, right before lactate takes off).