The answer is definitely no. If you see an apparent peak ("Overshoot") in an amorphous polymer sample just around the glass transition in first heating, it is most probably an enthalpy relaxation phenomenon. It appears on glassy samples stored for longer time near to its Tg. This peak disapperras in the second run.
I agree with Dr. Gyorgy Banhegyi, total amorphous polymer fail to rystallize or to maintain appreciable low degree of crystallinity. This is due the architecture imposed by the molecule which does not allow for chain regulation and folding, of course under thermal conditions. However, for the stress induced crystallization (shish-kebab arrengement) the situation may different, and for me this is left more to the experimental investigation rather to a tentasion background. Regards