Yes, it's possible to do authorisation over broadband and other IP connections (e.g. mobile GPRS). There are two main ways to do it -- either replace/upgrade the terminals so they connect to broadband directly, or install a "bridge" device that sits between your existing terminals and your broadband router. The advantages are, as you say, reduced line rental costs, and faster authorisations. Security isn't an issue as an encrypted tunnel is used.
However, I'm not sure if anyone is offering this to small merchants in Ireland (yet.). You can't roll your own solution, as you need a processor to accept your "cardholder present" requests over IP, and route them to the provider of your merchant account.