Is there a naturally occurring DNA polymerase that does not require a template?

This question is just nasty - but it does make you think. The enzyme TdT (Terminal deoxynucleotidyl Transferase) catalyses the addition of nucleotides onto 3' DNA ends without any template. It is therefore considered a DNA polymerase. It is found largely in B- and T-cells. Remember it as you learn about lymphocytes in Immunology. Then there is the whole issue of Translesional DNA polymerases. It's a bit of a stretch to consider the contiguous strand sitting under the active site a 'template' if there is no base there.