Let's see. When I installed my DSL modem and a linksys router for the ethernet set I had to put filters on the other voice lines to filter out the dsl noise.
It follows then that you should be able to install a DSL modem on the second line. It couldn't really hurt anything to try.
But, given the choice, I would do like the others recommend and set up a wireless access point and put a card in the second unit, then the location of the second unit would not be limited to where the phone tap is.
Regarding that DSL. I have DSL and mine uses 2 wires of a 4 wire cable and the other 2 wires are for the phone. In my house each phone outlet has a separate dedicated 4 wire cable taken back to the box on the outside of the house. I think this is fairly standard, at least in newer houses.
So to hook up a modem in that other room he may have to go to the box outside and find the right wires to that other room and connect the extra pair of wires to the proper terminals for the DSL in the box. And then of course he would have to connect them properly at the phone outlet in that room.
If he capable of doing this?
Just a thought.
If he can do that the wiring it might work but I don't really know.