Yes, whether or not you are immersed in still, motionless water, being showered by a … shower, or rainfall, or hose, being swept along by a river or undertow, or covered in snow…
The primary thing that triggers a human response to sweat is just your internal body temperature.
It doesn’t matter how or what is transmitting heat to you, so long as your body is generally above a certain temperature threshold, you will sweat. Go below a certain general threshold and you will begin to shiver.
Exactly what those temperature thresholds are vary from person to person, based on your genetics, the climate you are used to living in, what kind of fitness level you have, whether or not you are currently sick and fighting off an infection… etc.
Generally speaking, I am seeing that humans begin to sweat when their immediate surroundings are 32C or about 90F, but again, different kinds of people used to different environments will have somewhat different thresholds.
So, perhaps thats a rough approximation of how hot the water of shower or bathtub would have to be for a roughly average person to begin sweating while bathing.