Technically you could use the LAN infrastructure, but you wouldn't be using the LAN itself.
Ethernet cables use pin numbers 1,2,3 and 6, while telephone uses 4 and 5.
So, yes, you could use the same cable, but if that network point was plugged into a hub, your answer would be no.
We use this kind of setup at work.
We run cat5e ethernet cable all over the show, with at the very least, 2 network points per office. One point is hooked into the switch in the riser shaft, and the other one is hooked into the PABX, via the same riser shaft.
You can switch between them at will, provided you make the changes in the riser shaft too. Although it's been done, it is NOT a good idea to run a telephone signal through a live ethernet cable (by splitting the pairs), as the ring voltage is - i think - 24 volts, and will seriously kill any ethernet connection whenever the phone rings, due to interference.
As for using skype - I am not an expert, but I believe you can get adaptors that convert your analogue phone into a SIP capable phone, so then yeah, you could plug it into the LAN.
