Unlocked note8 will work with tmo and pcs. Locked note8 on tmo will work with pcs. To get carrier updates, phone must be active to branding carrier. Sent from Verizon note8 flashed tmo on metropcs recieving full updates and working great!
Although that "might" be true in this Note 8 case, its not always the case that carrier updates only occur if the phone is active on the branding carrirer. The unlocked ATT S8 I had was being used on Metro PCS (running an ATT official ROM) and when it was actually active on the non-branding carrier (Metro PCS), Metro PCS updated the (ATT) ROM to Oreo with an official Metro PCS ROM (the Metro PCS logo appeared at boot time; and the ATT logo was gone at boot time; also the Metro PCS specific software was present after the update; the ATT specific software was gone). I was pretty surprised Metro PCS updated an ATT branded phone (S8), but that's exactly what happened. It wasn't happening on my note 8 so I downloaded the official Note 8 ATT ROM and manually installed it (and am running it on Metro PCS). I haven't gotten any new updates (including any minor security updates) from Metro PCS since I installed the ATT Oreo ROM. I don't have the S8 anymore, but since Metro PCS updated the ATT branded S8 to a official Metro PCS Oreo ROM, I"m sure it will continue to get updates. I think the problem is simply that ther aren't any official Metro PCS Note 8 ROMs while there are official Metro PCS S8 Roms. I might try flashing a TMO official Note 8 ROM to see if updates happen after that, but might not mess with a good thing. My Note 8 is running great with this ATT Oreo ROM on metro PCS.
Also, an unlocked ATT Note 8 will work on ATT, TMO, and Metro PCS at the very least.
Verizon phones will not work on Metro PCS, Tmobile, or ATT as they use GSM *UNLESS* it's a Verizon phone with not only the Verizon CDMA radios, but also has the GSM radios used by ATT, TMO, and Metro PCS. My Verizon branded Pixel XL actually has both so I could run it on Verizon, TMO, ATT, and Metro PCS.
At least this is how things used to work. Things change all the time.