Solidworks cosmos meshing - does element tolerance affect the results?

Yes, if the mesh tolerance is nor small enough, the mesh will not map well to the part. Past a certain tolerance it makes no difference. For example in the part below there is no difference in mesh between a tolerance of .01 and .001, but you can see the difference between .2 and .01.

  1. Step 1:

    .2in tolerance

  2. Step 2:

    .01in tolerance