No that won't work as the international dialling code from Jamaica is 001, not 00 (the assumption that its always 00 is very much a British thing).
Change any Irish numbers you wish to use to a +353 pre-fix then the 8x, dropping the preceding 0, where x is 3/5/6/7, as appropriate. This will work from any country in the world (with a compatible mobile network, the exceptions being places like Tunisia).
When i was in america last year that what i did and it worked fine. Saved the effort of having to go into my phone and change the persons numbers. After the first text i just replied.