No.  In order to receive both fax and voice calls and messages successfully, the external TAD (telephone answer device) must be plugged into the jack on your Brother machine labeled EXT. Your machine cannot work properly if you plug the TAD into a wall jack (unless you are using Distinctive Ring).

When someone dials your telephone/fax number (to send a fax or to speak to you), all the telephones (including the Brother machine) will ring according to the number of rings you set on the TAD (telephone answering device). If you do not answer the call, the TAD will answer. As your outgoing message is playing, the Brother machine is in the background, silently listening for fax tones. If the Brother machine  hears fax tones, it will automatically go into the receive mode. If the Brother machine does not hear fax tones, it remains silent, allowing the caller to leave a message.
The call must come through the fax machine into the answering device. This is done so that the fax machine can monitor the call for CNG (fax) tones or the Activation Code.