Yes, assuming 100M or lower Ethernet, where only 4 of the pins are used. Gigabit uses all 4 pairs (if you have gigabit-capable hardware, you'll probably need to force it to negotiate a lower speed). Telephony normally uses pins 4&5, which won't be connected if you wire for 100M Ethernet.
You need to connect pins 1&2 and 3&6 using wires from the same pair on each socket. (At Ethernet frequencies, the twisting of the pairs matters, the colours aren't just for convenience.)
So, on one set of connectors you'd connect the orange and green pairs in the normal manner. On the other, you'd use the blue and brown pairs to connect to the pins marked in orange and green respectively.
If you're crimping plugs, it gets fiddly as you'll need to stick some dummy wires in there to make everything line up properly.
Stick labels on to warn that you've done this, lest someone get confused by it not working properly in future.