And what the image is projected on has nothing to do with the DoF either. DoF is determined by aperture, focal length, and distance to subject. That's it.it doesn't change when projected on a strip of film, a CCD, a CMOS, or frosted glass. Different GG elements can make the bokeh appear different and make it look as if it is effecting the DoF but mathematically this isn't possible.
If what the image was projected on (the size) didn't matter, then there would be no need for a 35mm adapter. As this would mean you should get the same depth of field on a tiny video camera as you would a super 35mm film camera (eg: same focal length (zoom), aperture, distance to subject). BUT YOU CANNOT!
What you said about zooming in on the GG is right: it will not technically change the depth of field, but visually this could magnify the effects of the dof eg: by emphasising a shallow focal point, much like magnifying the 35mm image on the GG emphasises this dof instead of 'squashing' it directly onto a tiny camera sensor. Hence why larger video camera sensors have a more evident dof (opposed to smaller).
