I don't think sweat will be a problem.
I've used them for a few months going to the gym and store on a daily basis. So far they show no signs of wear, melting adhesive, disconnection, etc.
A few years ago I used the adhesive backed insignia cloth on some kneeling/sit pads for backpacking. The insignia cloth went on one side of closed cell foam so pine needles and debris wouldn't penetrate the pad when I used it. These pads have been used extensively and show no signs of wear, delamination, adhesive drift, gooing, etc. I've even run them through the washer a few times.
The sweatiest application Ive used them for is on the side of my backpack that goes against my back. There is a reinforcement patch there for a strap that connects to the fabric. This area has been saturated in sweat many times, for up to 8 hours at a time with no effect that I can see.