I wouldn't imagine it would. It just probably wont run very well. As I understand it, all the MAF sensor does is monitor the amount of air entering the motor. Therefore, it shouldn't really do anything too bad to the motor, but I have a feeling that if you drive around with it unplugged then it is going to run really badly. It'll probably throw a lot of codes at you and you may experience very poor fuel mileage. Hopefully somebody that know a little more about the MAF setup will chime in. I'm just using a MAP controlled speed density set-up.
Well, it will run on the "default" fuel maps which normally runs pretty well...it "could" over fuel the engine which washes the oil off the cylinder walls...major wear over time.