Okay I'm quite assured that a singlespeed chain will work just fine on my middle chainring from a triple (correct me if I'm wrong) but I'm thinking in terms of wear - to the ring.
Am I likely to mash the chainring quicker than normal?
Middle ring will work fine, as long as your chainline is good. If it's out then the ramps and pins etc on it might cause you problems.
As for wear - it probably will wear quicker than it would have done in a geared set up as you're only useing the one ring (instead of spreading the wear a bit more over 3). Also you may well end up generating higher torque through the drive compared to how you ride on gears, which might affect things.
But in my experience the main cause of faster wear in a ss drivetrain has probably been the fact that you tend not to clean them as often, as they just keep going with a top up of lube every now and again. Thicker non-ramped rings and stainless steel rings help negate all this of course.