Through purely deductive reasoning, I would say probably not.
The nervous system develops by producing a surplus of nerves throughout the body. Through feedback mechanisms, the excess nerves die off, so that by the time the baby is born, it has exactly the nerves it needs to control its body. (In premature babies, the “pruning” process is not complete, which is why they are so sensitive to touch and so forth.) This mechanism is why polydactyls have sense and movement in their extra fingers or toes.
Young children have some ability to regenerate nerve tissue and “rewire” the brain, but that ability decreases over time.
I would think that the ability of an adult to learn to control an extra artificial limb with the same ease as natural, non-extra, limbs would be limited to non-existent.
There is work being done to make prosthetic limbs that respond to the same impulses as the natural limb they replace. That is not the same as giving a person a natural level of control over extra limbs.
I don't imagine it any time soon, but I suppose little infants could be fitted with some sort of vest with 2 extra arms controlled by their brains. They might learn to control them very naturally and subsequently spend the rest of their lives with brains wired for 6 limbs.
That’s very interesting.
Thank you for the detailed explanation. I always enjoy learning new things.