Yea, my roommate landed his current model girlfriend this way. Met her in June, finally laid her in September, finally became exclusive in November. So they've been dating a little more than a month. It also helps that he's a trust fund baby so he can spend his money freely on her, and he has. He has taken her on a lot of fun trips, buys her everything, etc. and in return he gets to have sex with a hotty. It's like legal prostitution lol.
Anyway, point is all that pursuing and spending thousands eventually got her in the sack. And he's pussy whipped like a mofo. So I agree that chasing IS bad because it can be expensive and it can take a few months and I think anybody reading this knows that eventually this girl is going to leave when she gets bored of the gifts and he runs out of money (which he's about out of last he told me lol).
So yea - feel free to Chase if you got the money. It's legal prostitution. Don't chase if you understand that there are other fish in the sea.