Normal zinc serum levels are 66–110 μg/dL -- that's *A LOT* compared to possibly mercury values even if they were elevated.
Most zinc is bound to albumin, which is the by far most abundant protein in blood. Which means if there's more zinc it too will be bound to albumin for the most part (80-90%), meaning additional zinc won't be any easier to bind to for Hg than what is already there.
Given the MUCH higher amount of zinc already present in blood at any given time I don't see how taking zinc could possibly make any difference.