Yeah, I think the conversation style is the insurmountableproblem. Picking someone up at a bar requires some combination of being an interesting conversationalist, actively pursuing women with explicit goals in mind, and being able to read social clues about how you are doing. Chris can't do any of these things.
I get the sense Chris would struggle to distinguish between "I am just being polite enough that I am not a huge bitch" and "Say the word and I will take you home with me now". That alone makes it really difficult.
Someone would have to be interested enough in Chris to pursue him and explicitly offer him sex. I suppose stranger things have happened. But not many.