No, TDS meters do not detect chlorine. A TDS meter can only read things that impact the conductivity of the water, which most salts do. Chlorine doesn't do this.
“Stop using TDS as the measurement of water quality. Disinfection Byproducts like Trihalomethanes, Volatile Organic Compounds, METHYL tertiary-butyl ether, chlorine, chloramines, cysts and lead are the primary contaminants to Public Water Systems. They have no impact on the conductivity of the water. Yet these do not register on a TDS meter. And public water systems primarily supply from surface water that tends to have low TDS levels.” ( Water Conditioning & Purification Magazine, March 2009, page 42 )