Based on this article from the Catalyst at Brown University, yes and no.
After 295 observations, the results were in. Do you sweat when you
swim? Sort of. Swimmers averaged a sweat rate of 123 milliliters per
kilometer swum, but this number is significantly lower than average
sweat rates for other types of exercise (about a third of the sweat
rate for running and half that of cycling).
This article references an Australian study "Body mass changes and voluntary fluid intakes of elite level water polo players and swimmers." by Cox G. R., E. M. Broad and L. M. Burke, found behind this paywall. It claims that:
The calculated average sweat rate and fluid intake rate during
training sessions for male water polo players was 287 ml/h and 142
ml/h, respectively, with a rate of 786 ml/h and 380 ml/h during
matches. During training sessions for male swimmers, the calculated
average sweat rate and fluid intake rate per kilometre was 138 ml/km
and 155 ml/km, respectively; and for female swimmers, 107 ml/km and 95