You can use originatechannel in your button configuration and create an extension that will set the sip headers for auto answering the call, in freepbx the standard code for doing that is *80 if I recall correctly, so if your extension is number 100, you can put in originatechannel: Local/*80100@from-internal
So when you dial or perform any other action that will ring your phone it will set your phone to auto answer and pick the call right up.