The first 200 I did on fixed was the Man Of Kent a couple of years ago. I'd only been riding fixed a couple of months at that time. After the climb out of Charing, there's a section of several miles of gentle descent. By the end of it, I was starting to get cramp in my calves. But that was just not being used to spinning that fast for that long. I've done the same descent more recently and didn't have a problem with it.
I did the Fairies 300 on fixed a couple of years ago and that has some long, very flat stretches. Where a fixed gear comes into its own on terrain like that is when you have a headwind. I find it much easier to slog into a headwind on fixed. On gears, it's too easy to just select a lower gear and spin. On fixed, there's no wimping out. I did the Fairies 300 on gears the following year and was slower overall. I would recommend taking your fixed for your flat 200.
Longest fixed ride I've done is the Invicta 400. Not an especially tough ride, only one hill steep enough that I had to get off and walk, but I was a bit out of shape at the time and suffered badly. However, I know I wouldn't have found it any easier on gears.
The worst thing about riding that kind of distance on fixed is not being able to lift your arse out of the saddle and coast for a bit to relieve the pressure.
d.