Cant comment on the specifics as I am not familiar with the Eire method of wiring phones. All comments are based on my experience as a BT engineer.
In the UK, builder generally take the cheapest and easiest option which is to daisy chain the cables from room to room. They also tend to use 4 wire (2 pair but not twisted) rather than 6 wire (3 twisted pair) which is the BT norm or 8 wire ( 4 twisted pair similar to CAT5)Now the phone down stairs works fine but the lines upstairs which I intend to use for broadband do not work! Is it a big job to get the points upstairs working (even though points are there but not connected). Are all connections (central telephone connection) contained usually in the attic? Would it be possible for a general Joe to connect up the points upstairs?
When the line is initially provided it would normally only be connected to the first socket as this is the demarcation point between the network and customer wiring. If the other faceplates were installed and enginner was supplied with tea and biscuits then all sockets would work when the enginner left (In my personal experience anyway )
As to whether Joe Public could work on it, I dont know the Eircom specifics but the BT NTE5 was specifically designed to allow customers to connect their own wiring to the line.
You can have a VOIP connection anywhere you can get your computer network to. The cable to your phone sockets almost certainly isnt CAT5 so is unsuitable for a computer network but a VOIP Analogue Terminal Adapter that allows a normal analogue handset to be used could be fed over that cable.
Hope that helps