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.