Putting 700c rims on a Varsity sounds kind of questionable with the existing brakes. Even with extra, extra long (like 75mm reach) calipers it would be a stretch, then your marginal braking would probably be even worse. Some of us need to figure out a way to build up mtb disc brake hubs for 120/126mm rear triangle old school bikes and rig up the calipers, rotors and brake levers that would be required.
Man that would be interesting (though not historically correct) and would work much better than the original design. Then you could run 700c tires and have a huge selection of tire widths and tread colors.