Please keep in mind that I don't know much so use small words and talk slowly when helping me out.
At work we have our network set up in the following way:
Our internet comes from AT&T U-verse which plugs into the back of their AT&T router. We have that set up to get public IP addresses and pass them through to our firewall router. All of our computers and servers sit behind this firewall. I do not fully understand this or if I'm explaining it correctly. The AT&T router is then giving out its WiFi signal which I can connect my iPhone to. I can't access the firewall from my iPhone, mostly because I don't know if it's even using WiFi (everything is wired).
Since the AT&T router is only handing out Public IP addresses, can I still connect my iPhone to it and "safely" use my phone?