Since nobody has answered, I'll take a stab at an answer.
Two wheeled vehicles are very dependent on such things as the frame geometry and weight distribution for their stability. You'll want to read about rake and trail. If you are decreasing the wheel size, you'll probably want to increase the fork rake in order to maintain the same trail. If the overall weight of the vehicle being designed is similar to that of the R3, you should get reasonable performance from the forks and rear suspension.
My short answer will be yes. With a welder, some skill, and enough ingenuity, you can make anything work. One of my shelved projects was going to be making a 250cc Ruckus. It was going to use the rear swingarm and suspension from a Honda Helix, just shoved into the frame of a 50cc Ruckus.
But, like johnnyvee said you'll probably end up having to tweak things as you go along to make it work in a safe manner with decent performance.
Sure. A person can make anything fit into anything. Radial aircraft engine in a bike frame? Done. In line four engine in a snowmobile? Done. Motorcycle engine in a Moped? Done. However, you're going to have to think 'outside the box' as far as engineering goes. Like Johnny said, things will have to be changed in order to make it work. But it will work if you have enough creativity, and patience.