In Ireland without visa, how to legalise

I was wondering what would happen in the following situation.
- Irish man marries his Filipino girlfriend and applies for UK visa.
- Is granted UK visa and the both fly to Northern Ireland.
- They cross the now open border with the republic without a visa.

The question then is, now that she is in Ireland and married to an Irish citizen is she more likely to be granted a visa to stay.
Also, if/when she has a child in Ireland would she be more likely to be granted a visa as her child would be an Irish national.

Hi,

If you bring your wife illegally into the country, it will take time to get her sorted:
http://www.inis.gov.ie/en/INIS/Pages/WP07000024

You will still be required to be able to support her, and she will not be entitled to be added onto your social welfare claim without permission to remain from justice.
If she had an irish citizen child down the line, applications for that also take years to process... You can read up all the queries people have in relation to Zambrano.