It's not as tough as you'd think. According to my computer I average 40 miles a day over 3 hours of riding, which is 13 mph. It's so little that in order to get in shape for racing, I have to work out for an extra hour or two after work.

And eating/drinking while riding is easy. You'll also have plenty of downtime. Even on a busy day, you can make time for the important things. Most messengers like to screw around during their day, anyways. Being able to do that is a benefit of the job. Besides, even non-diabetics have to use bathrooms, eat, drink, etc.