When you say "stray current" I assume you mean in the dangerous form, which can cause death or injury and not stray current corrosion? If you are referring to electrocution risk, electricity returns to its source; inverters, along with generators and shore power transformers, when the source of power, exhibit this phenomenon. In these cases leakage will not travel through the water because it has no reason to, it's not a path back to the source. This is why an isolation/polarization transformer makes for a safer shore power installation.
Shore power, on the other hand, for all intents and purposes, originates at the transformer in the marina parking lot or head of the dock, and thus leakage will travel through the water to return to that source.
I have yet to encounter a verified case of electric shock drowning (ESD) or in water electrocution from an inverter or genset, if anyone knows of a verified case please share.
Having said all that, inverter/genset and vessel wiring faults can still occur aboard, which can lead to electrocution, just not in water electrocution or ESD, and fire, so an ELCI on the inverter (and genset) output, along with GFCI receptacles, is still a good idea.