Every Alembic has a serial number. Even old ones! The oldest ones have it on the tippy-top of the peghead.
It may have been removed if it was stolen, it may have worn off like Keith suggests from playing. But it always has a serial number.
Aside from personal employee projects which are not Alembics and do not have serial numbers, there are a few instruments that were stolen from us before they were completed, and these of course never got a chance to be finished and get their serial numbers.