We study how connectivity influences the crystallization of fully flexible model polymers by applying a recently advanced amalgamation of the Green-function description of polymers, and the density-functional theory of simple liquids. Our calculations show that the model polymers only crystallize if the effective Kuhn length of the chains is sufficiently large compared with the range of the hard-core interaction between the segments. Also shown is the importance of bond-length fluctuations for the stability of the crystal phase.