Yup, you can do this. I did my first century a few weeks ago on a 31-year-old 5-speed mixte with "sit up and beg" handlebars. I didn't train - other than my 12-15 mile commute every day and the odd 35-mile ride on a Sunday. Lots of people told me "if you're fit enough to ride 35-40 miles comfortably (and not suffer the next day), then managing anything over that is totally about comfort".

Good luck with the ride! Hope it'll be the first of many!