You can not root [I assume autocorrect]/bootloader unlock the Pixel if you buy a carrier phone in the US. The carrier or network unlock status does not matter. They will not let you bootloader unlock it to put your own OS on. It does not matter if you pay 100% of it, not financed, etc. If it's sold by them it's disabled.

Examples: https://forum.xda-developers.com/t/unlocking-pixel-5-for-ver...

https://support.google.com/pixelphone/thread/156939637/pixel...

https://www.reddit.com/r/GooglePixel/comments/bmdtlu/tmobile...