I say, if it's in decent condition, why not? Your cash outlay will be minimal, and when you've painted it up all purty-like, you'll feel proud and glad to ride it, even if it is a little clunky.

I have heard that cottered cranks aren't the strongest for fixed usage, so if the bb is iffy anyway, you might just want to spring for a modern one and some regular cranks (which can be purloined from a newer ten- or twelve-speed). Also, Harris Cyclery has a pretty nice 27" fixed-gear wheel for about $100. I have one on my everyday ride and it has been smooth and problem-free for six months. Lastly, Weinmann center-pulls are pretty nice when it comes to actual stopping power and staying neatly aligned. If you can get away with just throwing some new pads on (Kool Stop salmon, of course), I'd recommend it.