Even that is not impossible, the rudder is a ■■■■■ though 
. I have flown using keyboard switches a couple of times to check something out quickly when I didn’t want to go through the effort to find and connect my joystick.
Problem is that the controls don’t auto-center like a joystick, neither can you really use any trim as you don’t really notice any “permanent” control forces. Therefore the controls probably aren’t centered when engaging the autopilot and keep overruling it, just check this weird autopilot bug:
Btw, also happens when using a joystick, just engage the AP and steer left or right and you will notice the in-sim yoke or stick moving in opposite direction.
I don’t know when this was introduced but the aircraft seems to have 2 sets of flight controls, if you steer left the autopilot steers to the right to compensate. Like you are controlling one aileron, the autopilot controls the other .
(Not exactly because that would make the ailerons either flaps or spoilers when deployed in the same direction, but you get my point).