The images have noticeable barrel distortion, and I could easily correct that with PTLens. Is prior correction with PTLens a good idea? Does ICE perhaps have a lens database itself and also do the correction? (I want to avoid double correction, naturally)
No, MS ICE does not have a lens database AFAIK. It really does not matter much since it has to distort the images to make features match and perform blending. In my experience success is generally high but not perfect. I would try straight with ICE first because any processing you do before hand always adds image quality loss. If it fails, then try it after correcting. Remember that when correcting barrel distortion you loose part of the image, so there will be less overlap for MS ICE to work with.