Do Polar Bonds Affect Molecular Shape?
Yes, of course they affect the shape. But only slightly so. More precisely, bond angles can change, however this does not change the general shape predicted by VSEPR.

For example, if two atoms (one with a positive pole, and one with a negative pole)  are connected by another atom, then the two atoms would make an angle that is smaller than the angle predicted by VSEPR. 

And also, polar bonds are capable of intramolecular bonding. Such as in protein-folding.  So they definitely contribute to molecular shape.