Well (obviously) you can't control attitude if it's not controllable.
My point was that AoA is not an input into attitude or thrust therefore not required to fly using those settings.
If there is a system on the aircraft which is taking AoA and stopping you from selecting and maintaining an attitude (like an errant MCAS) and you can't or don't disable it using the "AoA on the Fritz" drill then you are stuck. I'm doing my CAA mandated pitch training for [737] pilots this week so I'll keep a look out for it.
edited for grammar.