That’s not necessarily so. Note that Cumann Lúthchleas Gael is a genitive noun phrase. Since Gael is a genitive plural proper name, it’s a genitive definite noun, which thus makes its governing noun Lúthchleas definite. Because Lúthchleas in this phrase is “nominative in form, genitive in function”, its genitive definite status also makes its own governing noun Cumann definite. Since Cumann is definite, an isn’t needed, and so a leading “The” should be accepted in an English translation.
Even in brand-conscious Ireland, iPhones are in a minority (though you'd hardly know that by looking at RTEs app selection). Luckily, you can access the live RTE 1 Radio stream (and other RTE radio stations, such as RnaG) by going directly to rte.ie/radio1, or by using cross-platform apps like TuneIn radio.
You can also subscribe to the "GAA Go" channel to watch hurling and Gaelic football matches both live and on demand, as well as documentaries, TV shows and such; much of the content is in high definition (HD), and you can watch individual events on a pay per view basis, or get access to everything available on GAA Go with a season pass. As of right now (26Aug2018), GAA Go is also available via Roku (the Roku streaming device) in the USA, but you can also watch via computer at the GAA Go website, and I believe there is also a phone app. Some of the broadcasts are in English, some in Irish.
I have watched several hurling and Gaelic football matches on TG4, broadcast in the Irish language, on a show called "GAA Beo" (translation "GAA Live"); I have heard the Irish announcers refer not only to the name of the show, but also to the GAA itself exactly like that: G-A-A, pronouncing each letter exactly as they are pronounced in English. So, for whatever that example is worth, I know that at least some people (and in this case, broadcast professionals) say "GAA" even when speaking in Irish, but I doubt it's universally the case.