I have gone swimming with a under works double compression binder and a black t shirt, but I wouldn't recommend it, its pretty much impossible to pass with a shirt or a rash guard on in the pool because guys never wear those unless they are overweight, or surfers, plus you would have to get your chest really really flat because the water makes it cling to every little bit. but I can understand wanting to wear a shirt and binder to ease dysphoria, that's what i did it. You know, my dick of a 'friend' who know my trans status kept asking me, "well why are you wearing a shirt? why don't you have a bikini top?" oh hell no.
anyway, it wasn't a pleasant experience binding and swimming, its super hard to breathe and swimming is vigorous, I kept getting out of breath and had to tread near the side of the pool. but I still freaking lapped the douche bag who asked about the bikini top, while binding i beat his ass haha
anyway, thats just my opinion