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It's possible. S controllers have Bluetooth. But I've never done this having 2 Xbox One systems (one of them an S), and all my controllers are Bluetooth ready. I have 5 controllers, 4 of them for Xbox One systems (2 each) and one that's paired via Bluetooth to my Windows 10 Pro laptop.
The only way the OP can find out is to put a controller into Paring Mode and see if the iPhone 7 can pick it up. If the controller does not appear in Bluetooth to be paired, then the answer is no.
Question: Xbox one s controler and IPhone 7