Would things turn around for good if underdeveloped countries start to add value to their natural resources themselves without selling to the countries with good economy?
That's assuming that they can even have control of their resources. Being many of these countries being shitholes many of the resource extraction are done by multlinational companies that would interfere in the politics of the country to keep ores flowing.
Even without foreign funding though, being these countries have few stable institutions, it's close to impossible for them to start operations on their own.