Weapon element damage is overwritten by your skill damage. It has absolutely no effect on your skill's element - you can safely ignore the element on weapon's damage (two exceptions: there's currently a bug that enhanced damage affix on weapons only works for physical damage, which will be fixed soon; and if you're a wizard the weapon's element contributes to Elemental Exposure).
Weapon element damage is overwritten by your skill damage. It has absolutely no effect on your skill's element - you can safely ignore the element on weapon's damage (two exceptions: there's currently a bug that enhanced damage affix on weapons only works for physical damage, which will be fixed soon; and if you're a wizard the weapon's element contributes to Elemental Exposure).
So the answer to your question is: yes. :-)