With BW, people with the status rarely get upgrades even when booking directly through BW. So while your chances of getting an upgrade are low, it's not so much because you booked through a third party but because it's Best Western.

At Best Western, "every hotel is independently owned and operated", as BW always trumpets. Unfortunately, that means that the implementation of BW status levels is very hit or miss (mostly miss). The nice thing about this is that you don't get "cookie cutter" hotels with BW most of the time, since it also tends to mean that every BW was independently built, independently laid out, etc.