Yes, all products that are made up of 316L Stainless Steel or Titanium Stainless Steel are completely water/sweat proof, you can wear them at the gym or in the shower.
Products made up of 304 Stainless Steel can be exposed to water/sweat for some time although you should use them with care.
Products that are made up of White Copper or Brass are not water/sweat proof and you should avoid prolonged contact with water/swear.