Interesting little board!
Has more RAM than ESP8266 and should be able to address LEDs.
However, most examples only tell you how to use it with a separate MCU and AT commands (just like the ESP8266 in 2014 can you imagine not running application code on ESP natively today?)
There is also already a (Chinese and apparently quite unmaintained) Arduino core availabe for that chip.
Hardware wise this is definitely feasible but until this chip gets some more love from the Arduino community I’d imagine it would be quite hard to port all libraries required by WLED to work with the W600.