In glaucoma can eye pressure readings vary if the same machine isn't used every time and there is a different doctor performing the reading?

Yes: Many variables affect pressure reading including the machine type, the method, the calibration, the operator, time of day, breathing and ocular perfusion, position, etc.

Yes, but ...: We don't have a way of knowing the exact pressure within an eye without attaching a pressure guage to a needle placed through the wall of the eye-which is highly impractical. The common goldmann tonometer reading is affected by physical factors of the eye, how stable the patient & how tense the eyelid is, it's calibration and the accuracy of the person taking the reading. Done with care, it works.