Yes, of course you would be able to see all traffic that goes over the wire. It's called "wire sniffing" for a reason.
However, physically it won't be as easy as you might think it is. Your PC might have a socket where you can plug in a RJ-11 connector (your phone-line). But that doesn't mean your PC will be able to receive the signal. ADSL uses a much more complex encoding of the signal than old-fashioned POTS (Plain Old Telephone Service). Your PC must have special hardware that can deal with the ADSL signal. Then your PC must have software that actually understand the cell and frame format used (ATM/AAL5/etc). All that is not standard on PC. I guess you must buy a "ADSL-modem on a card" to build in your PC.
The result won't be as interesting as you might think.
You won't see your neighbors traffic. You won't be able to see anyone's traffic besides your own traffic. You might be confused by your understanding of ethernet. Ethernet is a broadcast medium. With ethernet, a packet is sent and duplicated too all other devices on a network. Network here means: "layer 2 network". Hubs, repeaters, they all copy packets in all directions. Bridges (aka switches) sometimes sent packets around, although most of the time they don't. But to keep it simple, you should view your ADSL connection as a simple point-to-point connection between your PC (or ADSL-router) and the router of your ISP (the so-called DSLAM). On the DSLAM all copper-wires connect from all your neighbors. But each copperwire is seen as a seperate layer-2 p2p network. Packets will be not copied from one copperwire to another, like ethernet does. So you won't be able to sniff other people's packets. You won't be able to see anything interesting.
Cable networks, now that is another matter.