Russ,
YES, all rifles chambered for 5.56 NATO WILL shoot .223 Remington ammunition with no problem.
The case dims are identical (SAMMI and CIP may show microscopic variation) ... it is only the leade, the area in front of the chamber that is relieved for the bullet, that is longer in the 5.56.
The .223 bullets typically have a shorter bearing area, so they use a shorter throating. Shooting the shorter bearing surface round in the long throated barrel is incredibly safe. You will absolutely have no problems shooting standard .223 ammo in the 5.56.
The reverse is not true. Not only is the 5.56 typically loaded to higher chamber pressure, but that bullet leade is working against you in this case. Do not shoot 5.56 ammunition in the typical .223 Remington chamber.
Not to confuse you, but there is a hybrid throating that is known as the "Wilde Chamber." The idea of the Wilde Chamber is to make the barrel safe for 5.56 ammunition and, at the same time, creating a decently short leade so that .223 ammo would shoot acceptably accurately.
Your Smith & Wesson M&P 15, no matter what configuration you buy, will have a 5.56 chamber. It will safely shoot both 5.56 ammunition and .223 ammunition.
By the way, I was the Lead Technical Feature Writer for Varmint Hunter Magazine for sixteen years, so I am vastly familiar with the .223 Remington, the 5.56 NATO, SAAMI and CIP.
Any other questions, simply ask away.
God Bless,
Steve Timm