Can one use a hemocytometer on a compound upright microscope?
Yes it can. You will want to use a thin hemocytometer and the working distance of the objective (20x) needs to be long enough to focus both the cells under the cover glass and the grid under the hemocytometer. Because you are looking at it from the top it would be helpful probably to have some phase on the scope to increase your contrast so that you can more clearly see the grid.

Hemocytometers are most commonly used with inverted microscopes because inverted microscopes are the most convenient microscope for performing tissue culture, and 's a commonly used to count cells when passaging or setting up an experiment etc, as they allow you to view cells in a culture plate. Upright microscopes require that you make a slide.