There is no reason why your normal telephone would not work after upgrading to ADSL.
You WILL have to install an ADSL filter to the telephone socket connecting your phone to the BT Box. You may notice a slight change to how your telephone voice sounds at the other end after you have ADSL installed. This is normal for ADSL lines and is not in anyway a fault or something that can be recified.
Your telephone Answering machine similarly will continue to work, but MUST be connected to an ADSL Filter before plugging into the BO Box, to stop feedback being recorded.