Definitely not the Void Elves 
In all seriousness, overall, I’d suggest no. This is purely theorycrafting, it should be noted. I don’t think we’ve been given a definite lore answer on this. But I don’t think golden eyes are an inevitability at all.
After the Sunwell was corrupted by Arthas, and then destroyed by Kael’thas not long afterward, the remaining elves of Quel’thalas found ways to cope with a lack of their traditional power source (to which they were all addicted).
Those who would become the Blood Elves siphoned magic from other sources, such as living magical creatures (like mana wyrms) and fel energy. Those who would become Void Elves much further down the line continued this philosophy, but specifically using void energy. Those who would become Wretched actually siphoned too much, and lost themselves to the addiction. Those who would become High Elves actually managed to quit cold turkey, and through sheer willpower, were able to quit entirely… surviving without a need to be constantly connected to a source of magic (though I believe it’s implied many of them died during this process).
With that in mind… many variants of elves have been able to last for a few years at least without connecting directly to the Sunwell.
So, my theory is this:
Most Blood Elves will eventually get golden eyes. Some will not, specifically warlocks and the like who may still be getting by on fel energy.
Some High Elves will eventually get golden eyes, though due to a lack of regular proximity to the Sunwell this will likely take longer than the average Blood Elf. That said, High Elves had an incredibly strong willpower to quit, and some may choose to simply shut themselves off from its power deliberately, as many addicts who’ve managed to quit an addiction will do. I suspect there are High Elves out there who fear the Sunwell’s influence, given that it remains firmly in Horde territory it could be something that is used against them.
Void Elves will not, in any form, get golden eyes. They are all using the void directly, which would very much nullify any of the effects of the Light. I believe this to be true of the original void elves who got partially etherealed, as well as the ones who’ve voluntarily chosen to study the void.