If it has any T-Mobile software on it, it will have to go through the T-Mobile channels.
Primarily, this is WiFi Calling (since things like MyAccount and that would be considered apps).
Also, understand that just because you purchase a device from other outlets doesn't mean you'll be getting Software Updates faster. The Nexus line has had certain updates delayed (search about the Nexus 6 with Marshmallow for folks with a T-Mobile SIM) because the Carrier requested it (in the case of the Nexus line, the suspicion is something related to Band 12 or something like that. I don't recall). You could always potentially install the Factory Image if provided by the manufacturer (in the case of the Nexus 6), but it could risk an incompatibility.
Manufacturers generally will honor the "can you hold your update from our users while we test this" request because they want to keep in nice with the Carriers so the Carriers will continue to sell their devices.
I have an unlocked PRIV which I bought on Amazon. Today I got February security patch/update from Blackberry. I have the device since December and have been getting OTA updates at the beginning of the month. I have WiFi calling and my device also connects to Band 12.