Another data point to consider; I purchased the Verizon version of the Pixel, but the initial setup was done with my at&t SIM and I immediately received the December 7.1.1 update via OTA. Even thought this was the Verizon version, the phone was never turned on nor setup with another SIM, but my at&t SIM. Perhaps this plays a role in terms of OTA updates (once you setup with Verizon SIM, or turn on the phone with Verizon SIM, the system registers the device as such). In any event, I can confirm that my Pixel from Verizon is working great with my at&t and received the December OTA update right away directly from Google.
UPDADE: January 2017 security patch update came in straight from Google OTA without any problems.