I assume you are comparing your situation now to a PSTN system where all the phones were wired?
Yes.

Essentially, you disconnect any external input to your house (phone company cable at the network interface outside your house) and then feed the ATA into any phone jack. All the phones in your house should work as before.
That's the perfect solution. You are saying it's not necessary to feed the output of the ATA at the external input to the house? If I'm understanding correctly, plugging the output of the ATA to any phone jack on the same pair will work as long as the external input is disconnected - right?