The IP address would be the Burner servers, not the end user.

Only if Burner is handling the outgoing phone calls (to your real phone number) themselves. Seems like you could bridge a phone call to a Twilio phone number to the end user's real phone with the <Dial> element pretty simply: http://www.twilio.com/docs/api/twiml/dial

You don't have to connect a call to your phone, you can just use Voicemail.