The Sig 556 is based on the 55x series, basically a take on their Swiss offerings. They also offer the 516 which is AR based. The 516 is still piston driven, but most parts are standardized with other AR variants. Sig also offers the M400, which is DI and basically completely standardized. I guess you could say they have a flavor for every taste.
With the Sig 556, aside from the obvious problem of the lower physically lining up with an AR upper, you have to take into account that the 556 doesn't have a traditional buffer like an AR. The buffer system on the 556 is contained ahead of the bolt in the buffer tube that rides on top of the barrel. So even if you could somehow solve the problem of the lower and upper mating, you still wouldn't have a buffer system, or any place for the BCG to travel into upon firing.