Is the BCG in the S&W MP15 mil spec?

Which M&P 15 are you talking about? If the Sport, then nope. It is a semi auto carrier, not the full auto carrier.

So none of the other components aside from the "full" carrier are mil-spec? In this particular case, what exactly is "mil-spec"?

Mil spec is loose enough tolerances to work in anything in any conditions.

None of it is truly "mil-spec". I used to post an article from one of the NRA magazines where Colt themselves even said that their rifles produced for the civie market are not mil-spec. If it isn't built to be sold to the gov., and doesn't go through gov inspectors, it isn't mil-spec.

Now, "mil-spec" the marketing term that we see, who knows what that really means. It could mean, in the case of Colt, all the parts used for the civie rifles are made from the same materials, to the same specifications and measurements, and undergo the same testing. Other manufacturers, it could mean that the parts from company A are made to the same measurements (within tolerance) and will fit with other parts.

If you are asking if your S&W bolt will fit into another AR-15 and function, then yes, more than likely.

I agree to a very large extent. Nothing more than a marketing tool which basically says, multi-source parts available and interchangeable ..........

Pretty much. I wish they would say something like "mil-spec dimensions". For example, the receiver extension, or buffer tube, is said to be "mil-spec" on the Sport. However, S&W would not tell us what the extension made of. They said it was "proprietary information", so even though the dimensions are the same, the materials used may not be.

Mil-Spec is a term often misunderstood. The specifications in a military contract have to meet those standards. Are they the best made part? Not necessarily, they just have to conform to the standards of the specifications. Does every part have to be tested? Only if the contract states it does.
Look at the Ford F-150 commercials from 2-3 years ago. The aluminum is military grade. What the heck does that mean? How many different type grades of aluminum does the military use? I'm sure dozens.
Civilian AR's are no different. Colt will say mil-spec, and I'm sure they do meet the same standards from the military contract. Doesn't always mean better.

Found the article again. Colt does not say mil-spec... And you are correct, mil-spec doesn't mean better. Look at all the different materials that are available today that weren't available back in the 50's when this rifle was being designed!

American Rifleman | The MilSpec Definition

As stated, in the civilian world (mostly us), it's a term used to convey the likelihood that most any part will readily be compatible with most any other assembly unless otherwise noted.