I second TT's experiences. My 350F had some chubby slicks on it when I bought it and it felt awful, I really had to fight it in the corners. I put some real skinny Avon tires (or o-rings as my friends like to joke) and boyyyyyyy is it ever a huge difference. It just came alive.
What model tire are you thinking about using? I have Kenda K270 tires on my XR, and they've been fantastic dual sport tires. I was thinking just the other day that I'd love to have a CL350 or something with these tires on. They wear ok on the pavement, and eat up pretty much everything other than wet grass. Not sure if they come in narrow enough sizes though.