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You can do this, but just two notes: 1) you still need a really good connection, not just something looped around something else, and all your fence mesh has to be contiguous and conductive; and 2) it does not work as well as a normally-grounded fence, because the animal ONLY gets zapped when it touches BOTH the hotwire AND the mesh fence. Although you can arrange things so it's pretty inevitable at some point if an animal is climbing the fence, it will usually get shocked later than with the other arrangement. IMO it is generally preferable to have a normal ground so the animal gets zapped sooner and runs away sooner, before getting as invested in exploring the possibilities of getting in.
That arrangement can be real useful on very dry or frozen ground, though, when a normal grounding system might not give much of a zap.
Pat