Class A can be described very simply as "current flows through the tube for the full 360* of the sine wave". It can never be driven into cutoff or it is no longer operating in class A. The same criteria applies for class A push/pull.
It (class A push/pull) is a very inefficient way to use output tubes. Without naming names, you often see amplifiers advertised as "class A push/pull" designs when in reality they are advertised as having too much output power for the tube types used to actually be running in class A. Even the Vox AC30 is not a "class A push/pull" design (though often referred to as, thanks Mr Aspen Pittman). It is simply a hot biased class A/B design.
I believe that Randal's simulclass designs do run the class A tubes in true class A. Here phase inverter drive to these tubes must be limited so as not to drive them into cutoff. Ok, rant over. Cheers