Tires make a HUGE difference. Definitely get some slicks on that bike before you join the ride. I think it will still be pretty tough to keep up, but it's worth a try. Did the person organizing talk about the pace of the ride or anything? I'm guessing it's probably a relaxed ride since it's only 13 miles. Did he say it would be tough in a negative way, basically saying don't come without saying that or did he say it in a way that was more it would be tough but you should give it a try?

I would say, get the tires and join the ride. Have fun. If they drop you, they drop you. No big deal!

One other option is to call around and see if any shops has road bikes they rent in your size. Then, you would really get a good feeling if you would like a road bike and hopefully you'll be comfortable on the bike.