Will it work for every telephone in the house?

The issue is having extensions throughout the house. And yes, there are a couple of ways to accomplish this.

Direct Wire
If the internet connection and modem are close to the telephone box where the outside telephone line enters the house, the entire house can be converted to digital or VoIP service. The "block" that contains all extensions in the house will need to be wired to the ATA via a standard RJ11 phone cable and the ATA will need to be connected to the internet modems with a standard RJ45 Ethernet cable. More then likely, the customer will need to secure professional help to accomplish this.

Cordless Phones
Most customers find it far easier to simply buy a cordless telephone system with a single base station and multiple extensions (up to 10) as shown below. The base station can be installed at the internet modem (regardless of its location) and extensions are installed in whatever room telephone service is desired.