This 100%. Though I would go as far as to say that having a weapon appropriate to a dungeon's level is crucial for a healer. You shouldn't be taking much damage so taking less damage is (almost) moot. Healing more and doing more damage helps everyone. If you can heal a tank to full with one Cure II rather than a Cure > Cure II (or whatever) then you save time and, generally, MP. Also it allows your Regens to heal more allowing more DPS down time. You shouldn;t really bat an eye at how useful a Weapon is for a healer. I would argue it's just as essential for healers as it is other roles because it effects DPS and healing.
