Families of SOs Community Group
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The CA RSOL site is chock full of Travel related issues.
http://californiarsol.org/2013/01/international-travel/
http://californiarsol.org/tag/international-travel/
This article / paper is a very good attempt at shedding some light on this.
http://californiarsol.org/2014/06/international-megans-law-rso-travel-issues/
It points out the difficulty of traveling to english speaking countries (US, Canada, UK, Ire, Aus, NZ). I do not recall anyone reporting on Ireland specifically but I would proceed with caution.
Another thing to be careful about is the advanced notification requirement in AWA states. I see no mechanism or requirement to report to foreign police while in another country.
I thought I remembered a page on the topic on http://www.oncefallen.com but I cannot find it now.
http://www.oncefallen.com/travel.html
For RSO specific travel to other countries, yes, the US government will generate a "green notice" and forward it to Interpol, which in turn notifies the visiting country. It is then up to the visiting country to take action or not. This is all done on the down low and the exact content of these notices is not known, but it appears that it includes reference to the sex crime conviction (seems only for those currently required to register) in addition to language that the individual is likely to repeat such crime.
Some countries will then deny entry to the traveling registrant based on this notice, and some won't. It is up to each country to decide who to let beyond their borders, as well it should be. The more the country depends on the US for whatever the more inclined they are to play along. Sound like most South / Central American countries, the English speaking countries, sex tourism (in general) destinations (Phi, Thailand, etc), will deny entry. No explanation, no appeal, buy a full fare ticket and go right back.
Since the US Government cannot restrict travel outright, this is the next best thing for essentially imprisoning RSOs in the US. Which is bizarre, because now all these 'horrible' people will spend their time and vacations domestically, alongside precious American and possible scantily clad children, at US beaches and such.
Everything I know is on the web sites linked. There are first hand travel accounts, and there are a lot. This practice is also trudging along in the US Congress under "International Megan's Law".
Do they run a check based on your license if not? Is it by name?
What if your last name changed and you've no social on your license can they still see your history?