personally, I'd say go for it! but that's just me and i'm a little crazy
I'm guessing that it runs from Wisconsin down to Chicago? That will be a pretty flat ride, especially along the shoreline, and the "Scenic" implies something more or less enjoyable (ie: recreational pace)! ... still, I'd start riding your bike whenever you get the chance and build up your milage over the next three months. Rails-to-trails should be more or less the terrain type of the ride. Set aside a weekend and see how far you can ride in a day, stopping whenever you need to. Set little goals, and treat yourself with coffee/ice cream when you reach a town or a certain point.
My mom and I started riding a few years ago on rails to trails. our first ride was 13 miles out, overnight stay in a B&B, and 13 miles back in the morning. if you make your training fun, you'll want to keep riding your bike! it helps too if you have a training buddy (the conversation is certainly better than riding alone! )
Definitely check with the people runnning the ride, and get their opinions too. They can tell you if they think its do-able (they will have had tons of experience judging the "do-ability" for different people) and give you tips on how to train. On charity rides, you get all types of riders, from families with little kids to people decked out on premo-roadies. Plus, they have rest points with FREE FOOD (my personal favorite part, next to the biking itself, of course)
If it turns out that the ride won't be the perfect one... I've heard of another ride that benefits Leukemia research from Gurnee, IL to Wisconsin. That one I know has a wide variety of people riding, and gives you options as to how many miles you ride each day (over two days). I've forgotten the name, but check out The Good Cyclist or Mikes Bicycle Rides for lists of charity rides in the IL/WI area.
good luck, and have fun!!!