Jazzyvee -
You pose an interesting question. For what it's worth, I'd answer it like this:
#1) Built by Alembic but with non-Alembic electronics is defintely a factory custom Alembic. The mixture would definitely be reflected on the birth certificate. In terms of resale valuation, it's higher than if the mods were made by a third party, but I would guess it would be lower than with stock factory electronics because, even with the birth certificate, it will be of questionable lineage, plus the cost retrofitting standard pickups and electronics would be so extraordinarily high.
#2) Started life as a standard Alembic, then retrofitted. It's still an Alembic, but it's a modified one. If the original electronics are no longer available or retrofittable, it's probably has very little resale value. If somebody was trying to sell this as an unmodified Alembic, then it will have zero value; as a modified one, it sort of depends on the modification, but will greatly degrade the price. The problem here is that restoration cost again - if you have taken $2000 of Alembic electronics out and replaced them with $300 of electronics, then you can assume you'll lose $1700+ off the top.
#3) Touched on what it should be called in the other two writeups. I do think that it's an Alembic in any case with qualifiers.
#4) You didn't ask about #4, which I think you're just as likely to see on eBay - What do you call a Fender Jazz bass that's had Alembic electronics installed (not Activators, but the real deal). I would say that that instrument's NOT an Alembic, but is modified with Alembic electronics and probably would sell considerably higher than what it was before, although less high than the cost of the electronics.
That's my 2 cents,
David Fung