My iPhone was stolen. I have AT&T. I did a factory reset, but believe my phone was turned off because I never got confirmation that the phone was erased. If the person who stole the phone took out my sim card, it will not connect to the network, which means they have access to all my personal info. If I have the phone put on blacklist, will this stop someone from being able to take personal info off my phone?
No. If they have the device, and there is no encryption enabled (e.g. lock screen PIN), they can read whatever they like from it. They won't be able to use it as a phone (they could use it as a fancy iPod if they wanted) in countries which support phone blacklists, or to access Apple services, but any data stored on the device itself could be accessed. This may include any data stored in Apple provided services, if the password for these was stored on the phone, and not been changed since the theft.
If the data on your phone was not encrypted and protected by a strong passcode/passphrase, whoever has it now will be able to access your information as long as the phone does not connect to the Internet.
It is good that you have requested a factory reset in case the phone does connect, but that cannot be guaranteed. Putting your phone's IMEI (identification number) on a blacklist does nothing to protect the data; it only prevents the phone from being used to make calls, texts, or use other cellular services in supported countries.
I recommend that you reset the passwords for every single account that you have ever logged-in to on your phone (Email, Bank, Facebook, Twitter, etc.) immediately, and then try to recall what else may be on the phone. Did you store any personal identification numbers or codes in the "notes" app? Did you take pictures of sensitive information? Think about potential remedies and do what you can to minimize the damage, assuming that the thief now has this information.
Once you have taken the aforementioned security measures, you should also realize that it is very possible that the thief would factory reset the phone himself/herself so that it can be sold as soon as possible. Perhaps they are interested in the value of the device, not the information on it. You should prepare for the worst (that the thief is exploiting your information) and hope for the best (that the thief just wants to sell your device).