We've done, let's see, four or five single-speed builds of old road frames, and I think we're about 50/50 on whether we've been able to swap in 700c wheels for the old 27s. If you have a spare wheel around, it's pretty easy to test.
Chain alignment should be a breeze if you buy a track wheel with a flip-flop hub; otherwise you might have to redish the old wheel to get the chainline neat, but we've actually had pretty good luck with chainlines working out okay. A bike shop can be helpful with that, but it has to be one that understands what you are doing. (Oh, man, did I get talked down to by guys who had no idea why somebody would turn a bike into a single speed on purpose.)
Speaking of bike shops, I shopped around for wheels online (the cheapest come from NYCbikes.com, but I've heard mixed reviews of their wheels and have never bought one myself) but we found our best deal locally. If 700c wheels won't work for you then your options are much more limited and you may have trouble finding anything locally, and in fact I think Harris Cyclery was the only place I found a set. You can also have a new wheel built up by about any wheelbuilder -- just ask. Harris doesn't have 27" rims on their custom wheel order page, but they said they'd be happy to do it when I asked. And it was not much more expensive than a stock wheel.
I have never heard of anyone removing the rear brake from a single-speed (as opposed to a fixed gear). We keep both brakes on all of ours.
I am working on a new SS project myself this weekend, waiting for my new frame to show up today so I can see if I need to stick with 27" wheels.



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