The "chlorine smell" is chlorine reacting to things in the water. Thus, if you rinse off before going into the pool, sweat, dirt, etc. on your skin will be rinsed off and will not cause as much reaction with the chlorine in the pool.

Pool water -- even really high chlorine levels -- where there is no Combined Chlorine (reactive chlorine) present has only a faint smell. The "chlorine smell" most people remember from being kids at public pools is the result of a lot of funky stuff in the water causing the chlorine to react.