I think it just depends on how comfortable you are with your hairdresser and/or how friendly the atmosphere is.

I've been seeing mine for years and she and I have no problems chatting. She's got a small salon in the back of her house, so it's always just the two of us and we chatter away while she's working. It's never anything major, but it is fun. Prior to seeing her, I had a couple of sessions with someone who was good at her job, however I wasn't really comfortable with her. We'd discuss my hair, but we didn't really chat all that much.