Image: Breakfast with Pandora = Food of the Gods
The word "ambrosia" in Greek means "immortal stuff." Ambrotos mean "not mortal," "not dying." In fact, one of the collective words for the divinities is hoi ambrotoi, or The Immortals.
What was ambrosia? Nothing specific the Greeks could imagine. It was just food for beings who don't die.
Scholars don't agree on the etymology of nectar.
The reader asked a very good question: "How dependent are the gods on nectar and ambrosia? Would they lose, if not immortality, then their youth/vitality if parted from a source of nourishment for an extended period of time (similar to the Norse gods and their dependency to the Apples of Idun)? And if not, then why do they need to eat and drink at all?"
William F. Hansen writes in Classical Mythology: A Guide to the Mythical World of the Greeks and Romans that nectar and ambrosia "maintain the gods in their ageless state," but I have never read anything in Greek mythology itself that says that nectar and ambrosia are necessary for maintaining immortality or that not consuming it would be problematic.
My sense is that the Olympians consumed nectar and ambrosia for the pleasure of it. This would make sense for the ancient Greeks, who had a perception of their divinities as immensely powerful, always blessed, dependent on almost nothing and no one.* Nothing interferes with or can impair Olympian immortality, so says the poet Hesiod, unless they swear an oath by the River Styx and go back on it. Even then they only stay in a deathlike coma for a year, and then are excluded from the community with the divinities for nine years.
During the year of the "breathless" coma, Hesiod writes, the offending god or goddess cannot "come near to taste nectar and ambrosia." This implies that nectar and ambrosia might revive him or her, but it may also simply mean that he or she cannot be in fellowship with the gods as usual.
On the other hand, the Titans, who were defeated by Zeus in a cataclysmic battle for world supremacy, did not die at the conclusion of the horrific firestorm created by Zeus' thunderbolts, but were mashed alive under massive mountains, where they lived on in chains and presumably had no ambrosia or nectar, either.
Based on all this, I don't think eating and drinking, or not eating and drinking, nectar and ambrosia would materially affect a Greek divinity's existence.
End of first part of post. For the really geeky among you, read on.
Greek mythology as a subject is like the subject of dinosaurs. It's beloved, and intricate, and there are a myriad details to study. And the people who study these topics tend to want to make sure they understand everything and that there are no inconsistencies.
Dinosaurs are an evolving subject (pun intended). Our understanding of them changes as scientists continue to examine and consider the fossil record. It hopes to be precise, but we don't know everything, and in the meantime the subject get tossed around in popular culture.
Greek Mythology is similar. It's not science, for sure, since messy, imprecise humans made it up. Nor is it theology, the way we think of theology as being mostly logical or at least able to be figured out to a point. But like the subject of dinosaurs it has been played with and changed and idolized and demonized, and Disney has made a movie about it.
Even the Greeks themselves loved their stories and changed them to suit their tastes and desires of the moment. So if you asked an ancient Greek whether ambrosia and nectar maintained the divinities in their ageless state, I'm sure you'd get a passel of yesses and nos and plenty in between.
The inconsistencies are what I love about Greek Mythology. They show that the Greeks were human. And I like human.
*Contrast this with the Hittite divinities, the family of gods and goddesses of ancient Bronze Age Turkey. They were dependent on offerings from the Hittite king for their well-being.