You need to mentally separate internet speed from wifi speed.
Internet speed is the speed of the connection from your ISP to your router and is basically out of your control.
Wifi speed to any device is the speed of your household wifi from your router to the device. But apart from the absolute limit set by your router’s wifi technology, is far more variable, but is within your control. Distance between the wifi router and the remote device and any obstructions such as walls between them.
The speed required to fully ‘feed’ the 4000t will be the same regardless of the connection method, wifi or wired. You can test the wifi speed at the location of the 4000t using a laptop or phone with a speed testing app and report here what you are getting.
The other alternative is the empirical one of “Try it and see”, If you get buffering, the connection is not fast enough.