YES, as in all pools.
Chlorine is an oxidiser and helps to break down organic matter like dirt and dust, sun lotions and body fats etc.
The Naked System DOES produce chlorine however, without stabiliser present in the water,
the chlorine levels in the water are expected to be approximately 0-0.5ppm.
If the correct TDS levels are being maintained in your pool the amount of chlorine in a Naked Pool is so minimal that you won't be able to taste, feel or smell it.
Here's a fun fact: You won't even need a shower (or bath the kids) after swimming in a Naked Pool.