Those giant bucket wheel excavators are also electrically powered, by cables. And they use up to 16 MW, so I wouldn't call it completely unrealistic.

Of course running them over some dirt is easier than through possibly moving water, but still.

cables can get pretty big, you could run maybe 75-90MW through a 66kV 1200mm2 Cu offshore wind array cable, maybe 500MW through a 275kV 2000mm2 cu export cable and 1.3GW through a 320kV hvdc bipole set of cables (2GW through 525kv HVDC!) - you would just have the minor inconvenience of convertors and or substations to deal with at either end ;)