Easy money here. The 223 was originally set up with bullets of about this weight (55 grains, to be exact), and yes, they shoot just fine. Lots of folks will set up a XC match-grade Service Rifle with a 1x12" twist, specifically to shoot reduced course matches or practice. Not only do they shoot just fine, but they'll also give somewhat better barrel life than the heavier bullets. Lighter projectiles will normally call for a somewhat faster powder than their heavyweight counterparts, and there's no exception here. I'd suggest W-W 748, H322, Benchmark, N133 or N135, or any of several others in this general burning range. With this combination, it's probably harder to find one that won't
shoot, than it is those that will.
For what it's worth, I know a lot of guys who load a 5.56mm version of "Mexican Match" by pulling the 55 gr FMJs from M193 ball ammo, and substituting a 52/53 grain bullet with the same load, no other changes. Generally shrinks groups down to less than a third of what the FMJs are capable of. A little something to keep in mind if you ever spot a deal on M193 ball and want something better than just plinking ammo.