While I'm sure there are speakers out there that would benefit from clay, I'm just not convinced it's worthwhile in all cases.
With my current speakers, the total weight of the woofer is 6 kilos. The weight is mostly in the magnet assembly. The moving mass is 33 grams.
I don't see that the 33 gram cone assembly is going to get the rest of the driver vibrating very much, especially since it's decoupled by the surround and spider, and the frame is clamped to the enclosure quite well.
There's more of a chance of exciting the enclosure walls via the air in the enclosure since there is much more surface area involved, but they're quite stiff in this case, well-braced, and the front and rear panel use constrained layer damping. So I don't see that this is really going to be audible either.
Covering things with clay would seem to work well when they are thin, flexible, and low mass. (It would probably work well on a speaker cone, except that the added mass would drop efficiency way down, and it's hard to apply it evenly. So it's not really suitable here either.)
I would recommend adding bracing inside your speaker enclosure if you're having problems with the walls vibrating. If the driver baskets are vibrating or flexing, put a brace between the enclosure walls and the magnet assembly. Tying the whole thing together will stiffen it and also tie all the mass together. The more mass, the less likely it's going to be excited by the cone or air in the enclosure.
I noted that the Salk speakers I've seen have stiff, solid enclosures that don't "sound" much when you rap them with your knuckles. Some other well-constructed speakers are like this too. I find it unlikely that adding clay to speakers like these will do much.
But hey, clay away if that's your thing.

A final thought... it should be fairly easy for an engineer to measure the movement of the walls of a speaker enclosure and figure out the actual acoustic output of the enclosure referenced to the output of the drivers themselves. I don't think I've seen that done anywhere recently (if ever). Then we could decide if this is actually an audible problem, or if we're straining at gnats.