It is commonly done. I work for John deere and we have a team dedicated to making sure that our products don't use conflict minerals, which if I understand correctly means mined with slave labor. I know for a fact that we have all of our suppliers traced 6 levels deep just to ensure that the whole chain is okay. We can put whatever want on the list, though we sometimes run into problems because we are too small to get any chip maker to care. (electronics are about the only thing that we are small players in, our list is in general common with the likes of GM so there is a lot of pressure potential suppliers for must stuff)
That's not what conflict minerals means. That term means what it says: that the minerals come from a (civil) war zone where people are killing each other over the right to extract them. That extraction may well also include slavery in some places, but it's not exactly the same thing.
While this is not exactly the same, the idea is very similar. I was very surprised to find out the corporations drill multiple levels down through the layers of contractors to promote ethical stuff. That's impressive.
Those multiple levels have proved very powerful. When the big earthquakes hit Japan industry all over the world was quickly able to figure out parts of the supply chain was most critical, vs what could be sourced elsewhere. (as I recall all the pure silicon for chips is made in Japan, so those factories were given all the electricity needed, while other factories that had competition elsewhere had to wait to get the limited power left). Companies that had their suppliers traced out that far were able to work stay in production much longer than those that didn't find out until months latter when things got through all the levels.