Sure, why not? Schmooze a little and tell them how much you enjoy your Foz, and that you'd really like a shirt. How could they say no? They used to give away free posters all the time if you asked for them.
Yeah you can get some good stuff from corporate, or even sometimes from dealers. Most dealers get tons of calendars, posters, tshirts etc when a new product comes out that just sit behind the service desk until someone asks for one.
I got a bunch of subaru t-shirts at the chase kiosk at the NY autoshow a few years ago when I signed up for a new scoobybucks card. They gave a free one when you signed up, and I went back at the end of the day and got a few that they still had sitting around.