Thermocouples are extraordinarily LOW impedance. They are two pieces of wire welded together.
It seems unlikely that leakage from that near-zero impedance circuit over to ground would have any significant effect on the measurement.
Fresh water is generally high-impedance (high-resistance) at DC. Water with impurities (such as sea-water) has much more resistance, but still many orders of magnitude higher than a thermocouple circuit which is near-zero.
The real question, IMHO, is how do you insert the thermocouple into the water stream? And what exactly is this water you are measuring? I wouldn't stick just any old thermocouple of unknown origin into drinking/cooking water. And maybe not into bathing/shower/laundry water either, at least until you thoroughly clean it, etc. There are special enclosed versions of thermocouples designed for use in potable water.
Of course, if you are simply thrusting the thermocouple into a running stream out of the tap momentarily, there probably is no sanitation issue.