In theory, telephony cable can be used to support 10/100 connections (not Gigabit) over short distances. If you can find a telephony cable that is not cut and is a "home run" between the two points you need to connect, and it contains at least 4 conductors, it may be possible.

Rj11 Adaptors | CPC UK

The answer is possibly... but without knowing more about the cable and the layout it is difficult to tell. For 10/100 Ethernet to work, you need to have a straight through connection of pins 1, 2, 3, and 6, and the other pins are not relevant/not used in this scenario. In the 568B color code, we need W/O-O/W (Pins 1&2) and W/G-G/W pairs (Pins 3&6) Pins 4, 5, 7, and 8 can be ignored (they are for PoE and Gigabit applications, which we are not going attempt with this type of cable).