The answer is yes and no.
First for the yeses -
1. If you are talking about via DSL (modem) or similar signal, it uses the same pair that your telephone line is on and it would connect to the input of the DSL modem, the output of the DSL modem (Ethernet would connect to your PC via a NIC. The pair on a T568B wired jack would be pair 1 (Blue/White)
2. If you are talking about using a dial-up modem, the telephone line would normally be on pair 1 (Blue/White) of a T568B wired jack
Now for the NO
If you are talking about an ethernet type connection it would require a minimum of 2 pairs, pairs 2 & 3 (Orange/White & Green/White) for either 10BaseT or 100BaseT type ethernetand all four pairs for 1000BaseT ethernet.
Joseph Golan, RCDD