I had about 100 shirts made up when I first went live with my site 8 years ago... I gave them away to everyone I knew... They are still getting mileage to this date... I still have friends that wear them to the gym... etc... and people always are asking "what is xyz.com" etc.. So I think it can be worth it... particularly if the shirts are cool or nice enough to where folks want to wear them out and about...
Go viral if you can aford it. Start giving away T-shirts that say: "Get this t-shirt free at www.whatever.com"
I have tried shirts, and I had 1000 pens printed with my url etc on them, and a bumper sticker....... results: nothing I mean I saw no increase in any traffic at all, after placing the bumper sticker on my truck, wearing the shirt and giving 3 others away, the pens I placed in every place I could, even at work, the laundromat, etc...... The only way such things work is exposure, maybe if you were wearing the shirt and you were seen close up on tv etc, that might work..... otherwise it wasn't even worth the printing costs for sure.
Ha... very funny... You are not going to see a bump in traffic from a few hundred shirts... but I think from a branding perspective it can last for years... It is difficult to see the return... but I think it was worth it in my case... Folks still talk about the shirts to this day and how they are always a topic of conversation, etc. It is hard to put a price on spreading your brand like that without gaining any direct sales or traffic that is trackable.
also it will be underneath the jackets for people in cold places. so you just get chance to advertise for a few months in summer.
I don't see how merchandise for a growing site will gain traffic. If I saw a bumper sticker on a car, I'd go "oh wow, cool a sticker" like I do with every other sticker I see, but as soon as I get home, I won't remember that url or that sticker, same with a tshirt, pen etc. etc.