What does someone gain from giving away his soul to the DO?

RJ told that "the Gray Men are slightly different [from the Ogier, who lost his soul]. But they also have given up their souls. They've given up their souls in a way. Already, their souls are gone. But it's happened in a way that protects them against this emptiness, as if they're severed from the physical and spiritual side. And the spiritual side is gone, but the physical side remains so there is an intellect in that body, but no soul." And that becoming a Gray Man is "a voluntary ahh.. rejection of your own soul. In that case, there are other skills, higher function. That's a matter of making a deal with the Dark One, and there are other prices to be paid from that."

Maybe the deal is that the Shadow provides them at least with a luxurious (immortal) life in the area around SG, where reality is largely shapeable by the DO. This way one would also ensure that the Gray Men are always available.