Sheldon Brown shows that a 700c tire won't fit on a 27 inch wheel.

The inner tube sizing will have more room to play with than the tire sizing. The 700c tubes are interchangeable with 27 inch, but the tires are not.

I tried exactly what you are asking about several years ago on my early-80s Schwinn Le Tour. Eventually I bent a rim beyond repair and ended up converting it to 700c wheels anyway. That would be pretty involved just to open up more tire options, but you could go that route.