No, He will say "My dad warned me about people like you" (despite his mum being a prostitute) That or he'll state "No thanks, I don't need any crotch rot right now".
Seriously, guys: It's the early 1900s. People weren't slutty or loose back then. Most normal people had really uptight ideas about sex outside of marriage. Women who showed off too much skin (like their belly or legs) were considered "loose" and "immoral". Most "good folk" didn't take up with whores or have sex outside of marriage, because that was sinful and shameful behavior back then.
I really don't get why so many people keep asking this question. Yeah, you could bang whores in GTA, but those all took place in the modern age. In 1911, the average person would avoid whores because they were very likely diseased or dirty.
Rockstar should have let you fool around with the whores, and then have your character die from the VD you get. Jeez.