In my experience, it only affects happiness. But note that happiness afects growth, productivity, etc. -- the need for entertainers reduces possible growth, and WLTKD reduces waste (which means more production). I use the luxury slider to (1) in times of peace, ensure WLTKD on the outskirts of my empire so I can build courthouses, marketplaces, etc., and (2) in times of war, to reduce the number of entertainers needed to keep my cities productive. (On the higher levels, a luxury slider at 10% or 20% is often needed in the early game just to keep size 3 or 4 cities from needing an entertainer).
EDIT: added ending parenthetical.