Yes, a single ended amplifier is an example of class A since the lone transistor is always in conduction.
It needs to be biased such that the transistor is conducting about 50% max current at 0 volts input because it can't swing past zero. This is normally accomplished by capacitively coupling the audio input and adding a DC bias circuit to the base which could be as simple as a couple of diodes forward biased, or a more complicated servo.