Not really, you have much better hardware for that, one that could actually do hacking (not that many people still use WEP these days since it's not the default anymore on pretty much all routers).
There isn't that much use for it, it's very small so people find it cool and spystuff like, it might have some uses like a cheap rogue access point detection system in places where you don't want any wireless networks but beyond that kinda nothing.
No, the Espressif SDK doesn't include the ability to do packet injection. They are likely going to completely remove the RFMON features if people start "abusing" them.
Cracking WEP/WPA on the go?