Yep. There are many ways to break a system. You can starve it for data, overload it, or choke it garbage. 800 watts or overload will work because the dynamic range of the typical WiFi receiver is fairly small (about 50dB) allowing any strong signal to cause the front end to rectify the RF and shut it down. This is called "blocking". However, such brute force methods are not considered very elegant and should be avoided if possible.
I forgot to mention that using an ESP8266 or Raspberry Pi is not really jamming. Instead, it convinces the WiFi clients and router to deauthenticate and disconnect, which is really a DoS (denial of service) attack. Either way, it will interrupt or block WiFi communications thus achieving the same desired effect:
Welcome to the dark side.