I guess so. Bitcoin is accessible by anyone, even poor people. Internet is the only thing you need and I think even poor people can afford to rent a computer. What you'll earn in bitcoins when you rent a computer is much more than the rent. It is clear that people who says that they can't do bitcoins because they are 'poor' are only using that as an excuse. They are basically just lazy and have no trust in themselves.
They way you seem to think about renting a computer in order to make people earn money is quite weird actually.
It's an internet connection that you need, plus a computer or other device that is able to do the same, plus a certain amount of understanding regarding Bitcoin.
Both internet and a computer require you to have money, and the poor people that do have some money, already struggle to feed themselves with that amount.
So how would you expect them to put that money into something other than food? Food is the most important thing for them, everything else is not important.
Just out of interest, let's say some people are able to do exactly that what you say. Other than signature campaigns, what will be their way of earning money with Bitcoin when they have zero skills?