700c's work fine on 27" bikes. the only issue is if you decide to run brakes. you need a brake w/ enough pad adjustment to reach the braking surface on the rim. some stock 27 brakes have enough adjustment in their calipers to allow a 700c wheel.. some don't.

to put it in perspective. imagine putting a 20" bmw wheel on your schwinn. the brake obviously won't reach the wheel. this is the same principle w/ a 700c, just not as extreme. in otherwords. the 700c wheel is smaller than a 27"