I thought it was like that, too, at first. Early articles read close to that. (Except, Apple says they all have to be connected to the same WiFi network.)
However, many people have reported since then, that you do not have to even be on the same WiFi network for it to work.
Reportedly, once the devices are logged into the same iCloud account and verified locally, SMS Relay works from ANY network.
I.e. after setup, you can then have BT and WiFi turned OFF on the phone, and the phone can even be miles away in another building, yet SMS Relay from a WiFi iPad somewhere else will still find the phone (via Apple servers as I noted).
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Again, this info is from many people reporting this capability. I'm going to try it myself later tonight if I get a chance. Link up an iPhone and iPad, then turn off BT and WiFi on the phone, and see if I can text another phone from the iPad. If anyone else can try it too, that would be great.