restore iphone by reinstalling firmware

iPhone 6 128GB

9.3.3 (13G34)

I want to restore my iPhone by going into iTunes and manually reinstalling 9.3.3 but I am afraid when I do that, I won't be able to access my phone without accessing iCloud. I just need to do that before going to APPLE store next week and getting them to remove this apple id.

When I try to sign out, from icloud on my phone it says my APPLE ID is locked and I tried to use the UNLOCK ACCOUNT feature by going to my email and resetting it but it seems ONLY my "APP STORE" passwords seems to change and not my SETTINGS -> iCloud password. They both have the same email address linked to it.

Let's just say I am out of town and I really need to restore my phone right now as there are some problems with it.

QUESTION: Does reinstalling of update require me to login to icloud ?