Yup.
Once the thing escalated, I'd probably realise that was all build up and be pretty creeped out. It would feel like stalking to me.
I was at a shopping mall once, and a guy asked me the time. I went wandering around the shops for an hour, then the same guy came up and asked me for coffee. "Have you been following me?" I couldn't get away from him fast enough. I have no idea how I would have reacted if he asked me for coffee on the first occasion, but the idea that this stranger had been following around for an hour still gives me the shivers. I know he was probably a nice guy, just a little shy, but yuck!