What if? That's the whole idea of it. It's what keeps highly profitable (to the employee) jobs churning... Nobody would work in the conditions needed for diamond extraction or sweatshop clothing making for example, if it wasn't for dire poverty.
Sure they would. People will do almost any job, if they're paid enough. This is why military contractors in war zones, Arctic crab fishermen, and prostitutes make a lot of money. This is econ 101; supply and demand. You know it too. You're (presumably) not impoverished, but you'd work in diamond extraction or a clothing sweatshop, if you were paid enough.
When I say "nobody would do it" I don't mean "regardless of any condition whatsoever". Even if there wasn't poverty involved, slaves would obviously do it too (and they were ones doing such things, historically, right until the end of the colonies -- and in fact still in several places, using various conscription schemes).
Nor did I mean "regardless of working conditions". E.g. if they make it as easy as pressing a few buttons, many would have no issue doing it, even for a low wage.
The idea is that people wouldn't do the job under the current working conditions AND wages -- if it wasn't for dire poverty. "Supply and demand" is not some contradiction to that, rather it is the very mechanism required to take advantage of dire poverty to give those wages.
And of course "supply and demand" is rarely a "natural" and "neutral" thing -- you can skew it in a thousand ways. From passing special laws to keep people down and prevent development, to killing people's farmlands to make them come to the big industrial city to find some low paying factory job to survive.