basically, yes, but the voltage required is very low (what needs to be large is the current), and you need to get the gold to dissolve. https://www.sciencedirect.com/science/article/abs/pii/S08926... is one of an enormous number of papers on the process, and ipmi has a careers video on youtube: https://www.youtube.com/watch?v=hAkWMdrLXmo. shandong xinhai mining equipment corporation has a bunch of youtube videos marketing their equipment for this purpose to gold mine owners
i haven't tried, but as i understand it, gold is one of the easiest metals to reduce; even trivalent gold is at +1.52 volts above the she: https://en.wikipedia.org/wiki/Standard_electrode_potential_(..., and monovalent gold is the noblest of all metals at +1.83 volts. that table doesn't have another reduction to metallic state until platinum at +1.188 volts, then palladium at +0.915 volts, silver at +0.7996 volts, mercury at +0.7973 volts, trivalent thallium at +0.741 volts, etc. the commonplace metals are far away from this: univalent copper is at +0.52 volts, the more usual divalent copper at +0.337 volts, trivalent iron at -0.04 volts, divalent lead at -0.126 volts, tin at -0.13 volts, nickel at -0.257 volts, cadmium at -0.4 volts, divalent iron at -0.44 volts, zinc at -0.7618 volts, etc.
in water you can't really electrodeposit metals that are much more negative than zinc because at -0.8277 volts† you start reducing hydrogen from the water instead of reducing the dissolved metal. so things like silicon (-0.909 volts from quartz), vanadium (-1.13 volts) and titanium (-1.37 volts from trivalent titanium ions) are out of reach. by contrast, the difficulty with gold is that you can't keep it from depositing—so you can't get it into solution in the first place
voltages like 0.8 volts may not sound like much, but that's because we're used to currents that are, compared to the number of free electrons in the metal, unbelievably small. 0.8 volts is enough to rip apart a piece of metal atom by atom. consider a mole of zinc anodically dissolving; every atom loses two electrons. avogadro's number of electrons is about 96485 coulombs, about 26.8 amp hours. so, if your other electrode is the she, anodically dissolving a mole of zinc (65.39 grams) yields 2 · 96485 coulombs · 0.7618 volts = 147 kilojoules, which works out to about 2.2 megajoules per kilogram. that's a substantial amount of energy
because of gold's extreme nobility people usually complex it with cyanide or thiourea in order to do things like electroplating. its standard electrode potential to go to metallic state from the dicyanide complex is only -0.6 volts. but i don't know what form it's in in the oceans
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† these potentials are all under standard conditions: unit activity for every reagent, 25° temperature, one atmosphere, etc. things like acidity and temperature can shift them a bit; https://en.wikipedia.org/wiki/Pourbaix_diagram is all about how they change with acidity, for example. but i don't think there exist conditions extreme enough to electrowin metallic vanadium or titanium