I just had my (1980?) Nishiki Olympic converted from 27" wheels (6 speed) to 700c wheels (with 8 speed). The bike shop had to file out the brake arms to move the brake pads down a bit, ground out the dropouts a bit to accomodate the new rear wheel, and I think they had to grind out the front forks a smidgeon too. I think the rear dropout grinding may not be necessary for you if you're going fixed gear as it was mostly to accomodate the wider spacing from the extra gears. I guess i you have a wider hub you might need more work - I have no idea what the width of the original 27" hubs were...

The new wheels work very well - or at least, they were till I got hit by a car a couple of days ago