From my understanding of FFF 3D printing, the glass state is usually used to heat the bed for better first layer adhesion. Other than that, does the extruder keep ex:PLA in a glass state for any reason?
Is the transition of the filament straight from solid to liquid for extrusion without any real regard for the glass state?
Note that the extruder feeds filament it doesn't heat anything, you don't want heat in the extruder. The hot end is the part that adds heat well over the glass temperature.
The glass transition temperature, the temperature where the material transitions from a brittle "glassy" state into a viscous or rubbery state, is always lower than the melting temperature. This temperature is of importance for adhesion to the bed; in a rubbery state the stresses are much lower than in a brittle state.
Is a thermoplastic's glass state relevant for 3D printing extrusion?
No, the glass transition temperature is not directly important for the extrusion, the extrusion temperature (where the filament is fluid enough for deposition and adhesion) is much higher than the glass temperature.
Yes, the glass transition temperature may play a role in the hot end in case of heat creeping up the cold end (usually some kind of radiator or heat dissipating element; usually connected through the heat-break), but not necessarily in melting the filament for extrusion. Heat creeping up with excessive retraction may cause filament to (partially or fully) clog and as such influence the extrusion.
The transition from solid to liquid is the important part.
The bed is heated for adhesion and kept heated for the same reason, but the extruder is a lot hotter and just performs the task of solid to liquid, the fans and ambient temperature cool it to solid.
Once a layer is solid it will heat up again when the next layer goes on it both from heat radiating from the nozzle and the liquid plastic going on it. This should give better layer adhesion.
