If so, would they nevertheless have reached final nirvana, on death?
It's a personal cause. You have to look at individual cases.
One can't say they all have reached Nirvana or they all haven't.
Part 1) Lord Buddha & Pachcheka Buddha & Arahant
As in Theravada tradition,
There are only 5 Lord Buddhas in this eon. Gauthama is the 4th, Maithree is the 5th. It will happen(coming of Maithree Buddha) like thousands of more years after Gauthama Buddha's Damma dissappear from earth.
But there are 3 levels of reaching full Nirvana.
- Lord Buddha / Sammasambudu
- Pachcheka Buddha
- Arahant / Rahath
There can only be max 5 Lord Buddhas in one eon.
There can be many Pachcheka Buddhas in one eon. But ones reach Nirvana while Damma from a Lord Buddha still exist, can't consider as Pachcheka Buddha. (because they didn't find Nirvana by themselves / other than if they didn't hear / learn Damma from that Lord Buddha)
There can be lot of Arahant in an one eon. But Arahant can only exist around Lord Buddha's Damma or Pachcheka Buddha's Damma. That's because they / Arahant learn Damma from others. (from Lord Buddha or Pachcheka Buddha)
So, Obviously if someone learn Damma from Lord Buddha and reach Nirvana, they belong to Arahant category.
However, everyone reaches Nirvana reach the same Nirvana. There's no difference in Nirvana.
Part 2) All Buddha
But because they all reach same Nirvana, sometimes it's considered as they all are Buddha.
So, why this confusion?
It's like saying all the people are same. One side it's true that all the people are same. But at the same time society contain hierarchies like power, money, influence ect. So society contain kings, wealthy, poor ect. So these hierarchies are true also.
Both are true at the same time.