That depends.
If you are getting a phone replaced through Apple, it could be new but it won't be NIB. Apple doesn't do that. You have the accessories already and they don't open new boxes to replace phones. It could also be remanufactured. Which may be better anyway.
Remanufactured phones receve a new battery, a new housing and all parts are tested. Those that fail are replaced with new parts and once it's all done the phone goes through a quality control check that is superior to the one that brand new phones go through.
There's no way to tell the difference between new and remanufactured.
Now, if your replacement is coming from carrier or third party insurance - who knows.