It's possible. I didn't look in to it that much. The Nordic 22 upper I plan to buy when they're finally back in stock matches the weight of my 223 upper pretty closely. Also, that way I get to use the same trigger and stock set up with the 22.
There are pros and cons to each approach. If the focus was primary marksmanship instruction, I'd go with the M&P15-22 because it's cheaper and a self contained purchase. I already have a 10/22 for that purpose (bought before the 15-22 was created). I primarily want it to practice with something close to my 3-gun 223 rifle without spending so much on ammo.