An interesting avenue depends on your interpretation of the CofA.
I don't have the exact wording to hand, but know that at least some in the FAA stress that the CofA is issued to an aircraft and is valid only whilst the aircraft *meets its design approval*
So if it was *designed* and certificated (certified) with a particular item, then it must have that particular item, in working order, at the time of flight.
They even took this down to the level of screws in cowlings and the little hinged canopy holder that one finds under the engine cowling of a new PA28. Even the stickers by the fuel tanks filler caps. If it was designed by the manufacturer to have them - then it must have them or the CofA is invalid by definition.
If you are talking about a UK aircraft, you could always look in the Air Navigation Order of course - but you knew that anyway.