If I understand your question, yes, a Restoration staff can do damage to an opponent, partly by itself and also according to any enchantment that's on it, such as frost damage or flame damage. But with staffs I think you have to keep the button pressed to maintain the attack; and as soon as your Magicka is depleted you need to release the button and let your Magicka level replenish itself. I don't use staffs myself-- I tried it once, on my main character that primarily fights with a two-handed sword, but I didn't stick with it because I didn't have any perks yet and wanted to spend my Skill Points on other things-- like Crafting.
Despite wearing heavy armor and fighting with a two-handed sword, my main character is actually a Sorcerer (go figure), and I can summon a Clannfear, Nightwing Matriarch, and Storm Atronach if I need to. The Clannfear in particular is handy in a fight, because I can call on him to heal me. The Nightwing Matriarch is supposed to do that, as well, but I find that it doesn't work as well as with the Clannfear.
Anyway, I always dismiss my summoned Daedra and non-combat pets when I'm not actively using them, because I find that they get in the way of being able to interact with people and objects. I wish other players would dismiss theirs, too, although I don't complain to them. But nothing is more aggravating than trying to interact with a banker or merchant, or use a barrel or crate or bag or treasure chest, and have somebody's Clannfear or Nightwing or Bear in the way!