As long as the wireless bridge acts as a ethernet cable as far as the Nest Wifi units are concerned, that should work, yes.
You could also throw some unmanaged switches in there to get more ethernet ports:
This will appear as wired backhaul for Nest Wifi, which you can read more about here:
Agree with everything @olavrb said, but would just caution that the secondary Nest WiFi Router unit will be acting as an access point, not the root of another mesh. It will effectively be a wired secondary, and those don't participate in the wireless mesh interconnect, and therefore other wireless mesh secondaries cannot be supported in other building. Otherwise, this setup does work. I haven't done it personally but I have heard from other customers who have successfully. Just take it all one step at a time, building the pieces up and testing in between each step instead of skipping straight to the final (and most complex) configuration.
Thanks for lending a hand, @olavrb and @MichaelP.
@jlewis2113, I wanted to follow up and see if you are still in need of any help. Please let me know if you are still having any concerns or questions from here, as I would be happy to take a closer look and assist you further.