It is much easier to use wireless than converting the phone line to Ethernet.

The phone line wire is not twisted as many as the Ethernet cable, like how any twist per meter. Therefore, it is more exposed to surrounding noise. You also need the phone wire with 2 pair of wires at least. However, I think the phone cable would be just 100BaseT.

Some modify the PowerLine adapter to use phone cable as transmission medium. You probably get around 200Mbps.

I'd say just use Wireless. Not worth wasting time and money on the old phone cable which may not work to your expectation.