Mexico was the destination for a chunk of Irish immigrants. So it isn't outrageous to think they could have gotten a bigger chunk. What Mexico needs to attract more immigration is stability and jobs. I think Mexico had historically suffered from regional labor shortage. With stability, and with it, a more robust economy/job market, there will be even more of an attraction for migration. Job availability, even more so than land availability, is the driving factor for immigration, so it is going to take more than just retaining Tejas to turn the tide.
USA is closer/cheaper to get to, and has the advantage of a familiar language, but there was also animosity toward the Irish.
Things have to go a lot better in Mexico in order for it to be THE go to place.