I was actually just thinking about this last night. From a strictly physical standpoint, yeah, the effective cone area is less, but my guess is that the designers have all of that factored in when they build the thing, and the size you're getting is more about the cutout needed for the box and obsessing over the diameter of the cone is something that we just need to get over.
But, yeah, if you were to extrapolate that and make a "15" that was four inches of cone and 5.5" of surround in all directions you'd have a serious drop of input, but let's throw some numbers on it. Let's say that you've got a 12" sub with about 1/2" of surround, and then another one that has a full inch:
3.14159*(12-1)^2 = 380sq
3.14159*(12-2)^2 = 314sq -> 314/380 = ~83%
An extra half inch of surround means an over 15% drop in cone area. But remember that the "rule of thumb" is that DOUBLING your cone area result in a 3dB increase in output (I don't have a source on this, just something that's been bandied about, so correct me if it's way off), meaning that ~17% of cone area you lose is gonna result in nothing substantial, PARTICULARLY if that big fat surround is there for a good reason, which I dare say is the case with Eclipse and others.