The Technicolor 3-D process I linked to earlier in this thread does just that. It is called an "over and under" process.
As the film is pulled down, through the projector, each frame is split in half, horizontally. The left eye's image is on top. The right eye's image is on the bottom. There is a prism box that goes on the front of the lens which passes each eye's image through a polarizer just as you mention. The viewer wears polarized glasses with the lenses rotated at 90º angles to each other. (45º to the left and 45º to the right, IRRC.)
http://www.technicolor.com/en/lo/3d-innovation/3d-in-the-theater
Digitally, one single video projector can be used to project 3-D. Theoretically, it is very simple to do. Practically, it's another thing, all together.
Basically they just double the frame rate and alternate the left eye and the right eye images. A spinning, polarized, optical glass disk is placed in the light path. It's on a stepping motor of some sort so that the computer "knows" what angle it's rotated at. When the disk rotates into the 45º-left position, the left eye's frame is projected. When the disk makes a quarter turn, the right eye's frame is projected. It sounds simple.
Two problems occur. First, only half the projector's light is shown on the screen at any time. The polarizer blocks half the light. Further, the left-right images are only projected one at a time. Digital 3-D projection can be very dim compared to film 3-D.
Second, that spinning glass disk rotates at several hundred RPMs. They have been known to shatter if they are not perfectly balanced. Just the glass, alone, costs a couple thousand dollars. This does not include any collateral damage from flying glass shards and it does not include the service call to make the repairs.
One thing about digital projection is that they are quite a bit dimmer, compared to a properly maintained film projector.
A film projector is supposed to produce 16 foot-lamberts brightness at the center of the screen. For digital, the standard has been lowered to 14 foot lamberts. At the edges, the brightness drops off to 12 ft-L. This is for 2-D. Cut that down for 3-D.
Most digital 3-D installations require a silvered screen to be installed as well as the polarizing box and the software to operate it. If you have a properly aligned film projector you might be able to get away with a standard white screen when you project 3-D.