no it wont even chamber, however there is a further nuance.
most current AR chambers are .223 / 5.56 WYLDE chamber meaning both will fit and function.
the problem comes from a straight up old school .223 being fed 5.56.
the evolved gas pressure is higher for the 5.56 round, and will probably work for a while, will put extreme use on the rifle and will eventually malfunction probably with similar results to the .300BLK problem.
a 5.56 can be forced to chamber in a 7.62 chamber, but is about 6mm too long so you will know theres a problem
7.62 nato of standard configuration wont fit the lede [ogive] of the 5.56 chamber unless you shove really hard with a mallet.
what you may see is a lower receiver stamped for 5.56 NATO
assambled with a 7.62 upper and barrel. this is proably fine for most aluminum lowers but i would stay clear of the polymer lowers or the skeletonized milled out lowers, for the 7.62