Maybe, but probably not.
A PIR or Passive Infra-Red sensor is based on sensing the difference in infrared radiation from a warmer object against a cooler background (or vice versa, sensing a cooler object against a warmer background) using a pyroelectric sensor (or detector). The pyroelectric sensor responds only to changes in temperature. It is insensitive to the steady background infrared radiation we are constantly immersed in unless that radiation is "chopped" with a mechanical object that alternately exposes and covers the detector.
A PIR motion sensor typically uses two pyroelectric sensors, electrically connected differentially, so their outputs subtract. A set of Fresnel lenses focuses an image from two slightly different points of view onto the two sensors. If an object that is warmer (or colder) than the background is present in both views but is stationary, there is no differential output from the pair of sensors. However, if an object moves across the field of view, one sensor will "see" a different level of radiation than the other sensor and their difference will produce an output signal while the object is moving.
The problem is that paper, coming out of a laser printer after passing over the hot toner-fuser roller, may not be warm enough, compared to the background temperature, to produce an acceptable signal from the PIR sensor. The emissivity of paper, even with toner on it, is very low so there is not much difference in radiation between the paper and the background. There is also the question of response time to distinguish two sheets of paper in rapid succession. Most PIR sensors incorporate a delay mechanism before producing an output, simply to avoid producing "false alarms." Depending on this "dead time," it may not be possible to distinguish between two sheets of paper.
It's certainly worth a try to see if it works. PIR motion sensors are inexpensive, so rig one up and see what you get. You might get lucky!
A better sensor, IMHO, would be an infrared LED paired with a photo diode (or photo-transistor) that the paper is forced to pass between, interrupting the infrared beam with each sheet. You can also modulate the IR beam from the LED emitter with a high-frequency square wave, and then demodulate the optical detector signal to reject ambient light if that is a problem in a brightly lit office environment. There are also commercial detector systems what will do for you, but you need to pay attention to how fast they will respond.
