No... no... and not as of July 26, 2002.
Some states may regulate it, but Illinois doesn't. We're not sure how that rumor got started. This comes up quite often because less than ethical suppliers try to use the marketing punch of "armor piercing" to sell more of their ammo. Since M855/SS-109 is more expensive than M193, some dealers go to great lengths to pawn it off. It is true that M855 was designed to increase penetration at longer ranges (500-600 meters) primarily to deal with the SAW issues, but don't mistake this "enhanced long-range penetration" design for "armor piercing." M855 is officially considered "ball," or standard ammunition by the military.
As if this were not enough BATF has specifically exempted M855/SS-109 along with .30-06 M2 AP.
NOTE: THE FOLLOWING CARTRIDGES HAVE BEEN REMOVED FROM THE DEFINITION OF ARMOR PIERCING AMMUNITION:
5.56MM (.223) SS-109 and M855 Ammunition, Identified by a green coating on the projectile tip.
US .30-06 M2 AP, Identified by a black coating on the projectile tip.