Not really, because the body self-regulates temperature by pushing out as much sweat as it needs to reach target temperature. A tool that facilitates evaporation allows the body to get by with less sweating. The amount evaporated will be the same, but the carrier won't be drenched. (PS: roughly the same, additional heat transfered from air to dry skin will need to be shed by sweating, but I doubt that this would make much difference compared to all the watts resulting from metabolistic base load, even in absence of physical activity)

Mandatory slightly related anecdote: on a summer drive through Morocco back when car air conditioners where a thing exclusive to America and the one percent I never felt sweaty as long as the car was moving.

Yeah I rarely ever feel sweat on my body when I run. It’s when I stop running that I get drenched and need to put a headband on.

(I live in a dry climate and generally don’t sweat much anyways, YMMV)

A few years ago I stopped sweating, almost completely. Trying to cool off is nearly impossible now.

I have an ice vest if I really want to go outside for then a few minutes.

Mirror clothing sounds like a dream.

Only in poorly ventilated enclosed spaces. But the sweat usually gets evaporated anyway only slower.

And when they are used outside, the added humidity is negligible compared to volume of surrounding air.