Do dendrites effect lithium-ion polymer batteries?
According to this Berkley Labs publication, "Roots of the Lithium Battery Problem: Berkeley Lab Researchers Find Dendrites Start Below the Surface":  


  Using X-ray microtomography at Berkeley Lab’s Advanced Light Source (ALS), a team led by Nitash Balsara, a faculty scientist with Berkeley Lab’s Materials Sciences Division, observed the seeds of dendrites forming in lithium anodes and growing out into a polymer electrolyte during cycling. It was not until the advanced stages of development that the bulk of dendrite material was in the electrolyte. Balsara and his colleagues suspect that non-conductive contaminants in the lithium anode trigger dendrite nucleation.
  “Contrary to conventional wisdom, it seems that preventing dendrite formation in polymer electrolytes depends on inhibiting the formation of subsurface dendritic structures in the lithium electrode,” Balsara says.  


So, it would seem that dendrite formation through polymer electrodes is indeed a problem, though it may require a "non-conductive contaminant" to initiate nucleation if these authors are correct.