Can that be done when the whole idea is to store a multiplier into a handful of transistors?

I have no idea. It makes my comment a statement posted as a proxy for a question, a question you correctly pose explicitly.

If it can, then deployment in a sea of gates can make a chip viable across model generations as weights change, inside some scale factor.

If not, unless the part is under a pinout and address model which can scale on the bus, and can be easily replaced, it makes the entire dependency a replacement, not just this part. So embedded use has consequences.