Honestly, I don't think he'd want a sex robot, precisely because a robot can't say no, can't be "wooed," and doesn't care that he's a songwriter who has kicked his disability's ass. There's no accomplishment in it that anybody could applaud him for. Any loser who could scrape together the cash to buy one could potentially own a sex robot, but you've got to be a real stud to get a hot human female (especially a celebrity) to fall for you. In fact, he'd probably be one of those guys who sees a guy with a sex robot as a loser, in the way that many incels see guys who pay for sex as losers.
He wants actual human women to fall for him (and onto his dick) as a way of proving he's desirable, successful, and has the ability to impress them. Yeah, he wants the physical experience of sex, but it's really about being able to prove to the world--particularly his birth family, as well as to other men--that he's just as able (if not more so) to be desired by the most attractive women. Getting a woman to desire him, who will not only willingly have sex with him, but also go out in public with him where he can show her off, is his thing. That's why he wants to go to dinner with every woman he creeps on--he wants to be seen in public, by others, in the company of a hot woman.
The women themselves are objects, their purpose is to provide sexual pleasure and impressing other men with what a "stud" Russell is. And yet, in a sense, they're no better than robots, in Russell's mind; he keeps using the same unsuccessful ploys to get their attention, because he sees women as "programmed" to respond favorably to them. But to Russell, that just means he has to put in "110% effort" to impress them, and in doing so he will be seen in an even more favorable light when he finally lands one.
It's not really about sex with Russell; it's about women as trophies he can display and brag about, and use as proof that he's been underestimated all along.