Probably not if carpet was laid over base. That stem in most cases has a nut tack welded on the end for your pole to screw into. If you have to I would take a razor knife and cut 4 slices from hole in center to edge of base. Take your time with a heat gun or hair dryer, heat one section of that carpet at a time and using a small putty knife try to peal it back to the edge. That way you could remove base and reinstall. Then get some Formica glue and put that carpet back down. You will have to find a stainless nut right size and have it welded on.. you would need your post screwed into not when tacking so it would be aligned.
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Charlie Weaver USN/ENC 1965-1979