If you were to remove it, it's going to depend on the type of account that's being used as to if it is going to delete the mail or not. If it's an SMTP server which updates on the server and not on your computer then it will remove them from your computer but if you connect back to the account, they will all be back the way they were before you removed it as everything is stored on the server.
If it's POP3 then you may lose the emails when you remove the account from Apple Mail. The easiest way to determine this is if you were to say check your email on your phone and then later go to the computer and see the same thing on your computer that you saw on your phone. Also if you were to check through say Apple Mail and then later go on another computer and check through the web browser and everything is the same, that is going to be SMTP, it is saved on the other server. If you read your mail on one device and then never saw that mail on the other devices then it is going to be POP3 as once your device reads the mail, then it removes it from the server that stored it till your computer got it.
All that being said, most of them now days are SMTP, but I'm not sure about AT&T and what type they are using. If you are able to browse it through the web and later still see it on another device it's most likely SMTP and you'll be able to remove the account and add it again with no issues or loss of mail that you currently would see on your computer.
