Another question about driver bias

Using the usual emitter follower driver feeding and emitter follower output stage, do the drivers contribute crossover distortion of their own? Or are they typically biased such that the opposite output transistor is on before the driver on its counterpart turns off. How does this work. My understanding is that they are not class A, unless they share an emitter resistor, but I am talking about the more standard version where each driver has its own emitter resistor.

Also, if the class A portion of the drivers signal swing is larger than that of the output transistor, wouldn't gm doubling in the drivers be an issue?

I never read about this, so I assume its not. Anyone care to explain the relationship between the drivers and the output when crossover happens?