First of all... From what i have tried.. It's same phone for all carrier..
It's just the numbers matter, i mean, the IMEI / ESN / MODEL NO... For Apple or cellular carrier it's had purposed, they can knew which is for which..
What i've tried is.. i bought locally an iphone 6 locked to ATT. I managed to unlocked it.
After restore and make sure it's unlocked, i put TMobile sim card, ATT sim card, even Verizon sim card with it. You know what..all works perfectly..
Even the data speed.. ATT , TMobile and Verizon all got the 4G LTE (what ever name they call it). I don't know about Sprint, i never want to touch Sprint...
So..based on your concern, i think as long as you bought UNLOCKED iPhone 6, it supposed to work on any network, any carrier in the world. Yes..if you purchased unlocked iPhone 6 from TMobile, they want you activated or used their service for 40 days, but..it doesn't mean your iphone is not unlocked. They just don't want to get people got away just like that without paying any extra..(this is what i think. It's all about business and money).
You can purchased from ATT, TMobile or Verizon or at Apple store, if you looking for unlocked iphone. Who ever had it in stock. Probably you already got your own answer, it's been more than one month ready.
There are one thing, i feel curious..why you should let your carrier know that you are using iphone 6 unlocked? You can not saying anything about it.. If you concern about the profile setting for your carrier, i believe you can got the info somewhere else. But, maybe you no need to, because it can update and set for it self. Hope can help..