Well, there's some practical considerations - getting the refresh rate sync'd up, avoiding or filtering moire patterns out, getting the colors and such just right, things like that. However, it's possible enough that most theater projectors already have DRM restrictions that shut the system down if you start fiddling with the image path. The password to authorize an image path change is only handed out to supervisors. Evidently, access to such codes were so uncommon that, during the 3D movies era of last decade, most projectionists wouldn't bother swapping out 3D stereographic filters for 2D showings because it would require getting management involved.
Modern cameras will actually automatically sync their shutter rates to any flickering light sources. As for colors, they are designed to let you apply lookup-table based corrections by providing huge amounts of color information you can correct later.
Crucially, this approach wouldn't trigger anything because all of the equipment would work outside of the projector. You would add the lenses and camera aligned and just after the projector. In effect, the system would take the place of the screen in the image path. I don't know of any protected image screen that can detect tampering.
