Hi @steelydev not sure if you are using a core or photon but yes listening mode is definitely blocking.
Not sure how WiFi.listening() would be useful either but there are a few ways to solve this problem
If you are on the photon see Implications of customized system firmware - Photon where @mdma shows a new feature that was added to the photon_043 branch. System event this works great for what you need.
If you are on a core the task is much more of a workaround. You can setup a timer based ISR that is enabled when you clear credentials this ISR would toggle your LED using @peekay123 timer library.
Good Luck.