I can't seem to find any reference to this scenario. I have the iPhone wiped, updated, and set-up with a new apple ID. But I would prefer not to activate it as that would require a dedicated plan. I use an Android phone. The iPhone is a device that my wife has abandoned that I am attempting to set up with an Apple watch which, in my opinion, is the best smart watch. I'm aware that I won't be able to see, respond to, or make phone calls, but to have the rest would be great. Who knows, I might even become a convert if things go well. :) I bow to those who have an educated answer. Thank you.
The answer is...yes, but you need to activate it first.
From a hardware perspective, if you have an Apple Watch 4 with watchOS 5 and an iPhone 6 running 12.x, you meet the bare minimum of requirements.
The short answer is you need a SIM card to activate and upgrade the phone. However, you don't need cellular service (well, maybe for a month). If your phone is "free and clear" meaning you don't have a carrier obligation on it, you are free to take it to whatever carrier you want.
In this case, to activate your iPhone, it needs to communicate over the cellular network once. After it's been activated you can disconnect your cellular plan and use it as an iPod Touch. Everything on with iPhone with the exception of both cellular and WiFi calling will be functional. In other words, you can use it to browse the web, but you can't make calls (including Skype). However as long as you have WiFi, the rest of the functionality that requires data will work; including your Apple Watch.
Can you do this without activating?
Sure. If the person giving you the phone doesn't restore it to factory defaults and you don't upgrade it at all, you possibly can use it without activating it but this seems like more trouble than it's worth. You basically need a SIM to operate the phone.