Would moving the cornea lead to loss of vision?

Likely. The cornea is the normally clear window of the eye, an important focusing element in your vision system. Exchanging a damaged or diseased cornea with a transplant to restore anatomy and/or vision is common. So, yes to your question if i understand it correctly.
??? The cornea is a clear covering over the colored part of the eye, the iris. It can't be moved. The conjunctiva is a clear tissue on the white part of the eye which is loosely attached and can be moved to some extent. While not advisable, not blinding to move it around.