And just so you know, the 15-22 upper won't fit on a real AR lower either. The main reason is that the from takedown pin lug on the 15-22 is too wide .
Finally, before you spend too much on a S&W M&P15, consider a rifle from Spike's, Daniels Defense, Bravo Company, or Del-Ton. As always research will be the best thing you can do.
*Aim small, miss small...