I used to work in a zoo and I can say that when I had the time (which, to be honest, was sometimes a rarity...) I really enjoyed chatting with "zoo/animal nerd" guests. Zoo people love our animals and love to chat about them and a lot of zoo people love to chat about, well, their zoo and other zoos too. I will say that this depends on the individual day because sometimes I was just toooooo busy to really stop and say anything, and also keep in mind that a lot of zoo people are "animal people" and not necessarily "people people" who are extroverted enough to have conversations with complete strangers. When I go to other zoos, I chat with the keepers as well (and mention where I work/ed) if I can tell they're not busy at the moment.
Usually chatting will not get you to a behind-the-scenes area, but you never know. My facilities were more relaxed about BTS tours, but I still probably wouldn't have taken someone I didn't know BTS. Many facilities, especially the bigger ones like SD and the like, have strict rules about BTS tours and you need to get prior permission from your boss, etc. to take anyone BTS.