I do not know of the Greeks themselves but we do know that people much later on took his meaning to heart of there being different 'ages' of men. In fact, Ben Kiernan would argue it is the first text written would lay in stone Western justifications for genocidal violence, creating a rudimentary racial theory that Medieval authors would rediscover and thoroughly take out of context as well as playing into Early/Modern concepts of idealization of agrarianism and 'the sturdy worker' (concepts which are all heavily present in the Armenian and Cambodian genocides and Nazi ideology itself).

However that notion of misinterpreting and taking out of context is important. This is not to say Hesoid was a genocidal racist. He lacked an obsession with domination or violence or subjugation in any way and was merely writing as a critique of commerce and as he saw as the lessening of mans virtues as an entirety.

However its connection to 19th and 20th century agrarian, 'sturdy worker' idealism, notably present in Nazi propaganda, can not be ignored. Nor can, even more importantly, its direct connection with Early-Modern conquistadors and settlers who used Ancient Greek texts, notably Hesoids work, to justify the supposedly non-agrarian Native peoples as 'barbarian' and thus not deserving of the land nor equal treatment. They would cite innocuous phrases like praising the "rich man who hastens to plough and plant and manage his household." He praised the "sturdy man", calling them "straight-judging men." This would come with a heavy dose of patriarchal tone as well when he would say things like "No arse-rigged woman must deceive your wits with her wily twitterings when she pokes into your granary" and then going on to compare men to productive bees and women to "drones".

However, to your question itself. Hesoid would, in Kiernan's words, "combine his notions of the sturdy farmer, devious woman, and deluded merchant with an emerging theory of race." Again, I do not know of Ancient Greek history explicitly, that is, if these people actually believed in this in its literal state. However the message of it was certainly believed and the message was that the more 'pure' the race, more agrarian they were. For instance the first 'race' lived in the golden age, when "the grain-giving soil bore its fruits of its own accord in unstinted plenty". Their, in Hesoids own words, "inferior" successors were distinctified by wasting time trading and waging war rather than, as the Golden Age of Man, "harvested their fields in contentment." The point, at least in the study I delve in, is not if they believed literal demi-gods existed. The point is that in their mythology, the demi-gods were redeemed in that their survivors live on the Isle of the Blessed where "the grain-giving soil bears its honey-sweet fruits." They were, at least, returned to their peaceful, agrarian, hard working roots in plentiful land. This in comparison to those before them, the Bronze Age of Man, who were "no eaters of corn."

This is an incredibly important work in the field of genocide studies to say the least. Hesoid would be the first time that cultivation, gender, race, and most importantly, extinction, would be connected. Yet it is worth noting, again, that Hesoid was not advocating extinction, but merely describing it. He explicitly said ". . .violence is bad for a lowly man; not even a man of worth can carry it easily . . . Right gets the upper hand over violence in the end." Violence is the major factor in his description of the Bronze Age of Man falling -- that they spent too much time fighting each other.

Yet, again, his work would connect these concepts of race to cultivation to extermination. Combined with Aristotles concepts of barbarism and 'natural slaves', which in 13th-17th century Western Europe meant someone not-Christian, all the justification necessary to exterminate hundreds of thousands of Native Americans became trivial. Probably my favorite quote to pull out on this is John Mair in 1519 when he said, w.r.t. the Caribbean Indians, who "live like beasts . . .the first person to conquer them, justly rules over them because they are by nature slaves." He would go on to justify this quoting Aristotle, saying as they rule over the Native, "the Greeks should be masters over the barbarians because, by nature, the barbarians and slaves are the same."

This would only continue to spread in philosophy in the 16th century. Creole thinkers considered the hemisphere a pastoral paradise, the "Garden of Eden". It was a pure agrarian paradise that was not being used by the 'lesser race' of man, the Native American, and thus they were wasting their opportunity. They would find biblical justification for their Greek supported bias by connecting the Native Americans to the Curse of Ham.The virtue "lay in the land, not peoples".

TL;DR:

Long meandering bullshit that doesn't answer your actual question at all but is at least related. I don't know if people actually believed there were demi-gods but they certainly believed in the moral of it -- that those who were non-agrarian were doomed to destruction and an inferior race. That the value is in the land first and foremost and how man treats it. This was 'hippie' from Hesoid but it would be brutally morphed to justify ideologies of hate and violence throughout the centuries following. Maybe not directly every time but certainly acting as the foundation of what everything following would be built upon.

My primary source on this matter is Ben Kiernan's Blood and Soil: A World History of Genocide and Extermination from Sparta to Darfur -- a spectacularly composed volume of, well, the title :P