Yes and no. There are lots of factors that come into play here Regular training causes you to sweat less when doing nothing, but you will sweat more when exercising.
One reason why this is the case is because training helps keep blood pressure low. High blood pressure makes you sweat more when you aren't doing a thing. Some fat asses are so out of shape that they break a sweat playing video games.
So, on the flip side, regular training will make your sweat glands kick on faster and produce more sweat during training to keep you cool as an adaption to to the stress on the body.