Of course it will work.  That is simple optics, and a set of
extension tubes will allow you to cover a wider range of close-up
shooting than a single fixed length extension tube.

    A bellows would cover an even wider range of focusing distances --
though with a zoom the greater magnifications might move your focus
point to somewhere inside the front elements of the lens. :-)

    I lose track of which camera you are putting this on, though the
55mm macro, and the 80-200mm zoom suggest that it might be older Nikon
lenses, which will not work with metering on the camera anyway for a D70
(if that is what you have).  The extension tubes would prevent that
anyway, unless you have an extension tube which completes the electric
circuit between a CPU-equipped lens and the camera body.

    The remaining question is how sharp will it be?  That, you will
have to determine by experimentation.  (You'll also have to learn to
adjust exposure for the extension, and I'm not sure how to predict that
for a zoom lens, which is trying to be everything for everybody. :-)

    But -- it will cost you nothing but some time to experiment,
unlike the days with film.  Just use the histogram to fine-tune your
exposure values.

    Enjoy,
        DoN.

Adding the extension tube will bring the close-focus limit of the zoom
in closer, so in that sense it "works".  That tube isn't very long, as
I remember it, so it won't bring the close-focus limit all that *much*
closer.  And the complex optics of the 80-200 probably won't stand up
really wonderfully to being forced to focus closer, either.  Your 55mm
with the tube will give you greater magnification and probably better
quality, but at shorter working distances.  

Or, the simple bottom-line version -- So play with it and see if you
like the results!