Changing your state of licence issue (SOLI - You'll get to know this term if ever doing it to the UK) to Ireland will not give you an IAA national licence, it will give you an IAA issued EASA licence. This is the problem with the 2 licences thing, because I *think* it IS actually possible to keep a national licence in one country and hold an EASA licence in another... I am not 100% sure about this but it is not relevant.
What it means in the end is that you aren't CONSIDERED to be an EASA licence holder, you actually ARE one, the same as before. It will just be administered by a different country/authority.
In theory Ryanair should have no reason to ask you to change your state of licence issue to Ireland. I believe that the only practical reason they does is that most/all their TRE's are under the IAA and thus would (again, this is what I am led to believe I am not 100%) require a briefing from the UK CAA/other authority in order to conduct LST's etc for a non IAA licence holder.