Mitchum
Deity
I've done some more testing, and you can fit another warrior in at the very start (i.e. worker-warrior-warrior), but it's not without cost. Specifically, 19 hammers and 12 GPP. Similarly NY can build a warrior by 2000BC if necessary, but I'm not sure yet that it is.
It'll be a long long time before there are enough cities on the map for the barbs to start invading, so it's just a question of exploring and defogging areas we really don't want a barb city to spawn.
Preventing barbs from spawning can go a long way to making our opening much easier and less stressful. True, barbs may not enter our cities yet. However, if we don't have access to horses or copper, it's very hard to move warriors out to spawn bust when there are already barb archers roaming around. We'd almost be forced to build a bunch or archers to slowly expand our fog busted area outward. If we get our warrior into position early enough, our barb problems would be much easier to manage.
I just thought of one additional advantage to early BW; we find out where copper is before we settle our second city. It's possible that there is a good, nearby city site with copper that may open up a possible axe rush.