Nope, you need to set-up your console with the country you're in or you won't be able to use some features. in your example the Irish user setting UK as a fake country, he will need a British payment card and will see prices in pounds instead of Euro.
As a migrant I am hugely disappointed in this lock. It's something trivial to implement (liberating locales) and a real problem when it's not. Say I'm a British working in Italy. I will want to set my xbox to UK in order to use it in my language, but then I won't be able to use the online store because I will need to use my British bank account instead of the one receiving money, the Italian one. Then I will want to watch some videos. the UK marketplace will show me British stuff but I won't be able to access it because it will likely be geoblocked. And if I want to look at the local unblocked Italian stuff I will have to change my locale to Italian, lose voice control and have the whole interface in Italian.
Not even going this far, in the US many people speak spanish at home and are likely to be fluent in both spanish and english. They will have to choose one language and get stuck with it. Choose one locale, get stuck with it (or delve into menus everytime you ant to access something in one language or the other). Same goes for Canada and Quebec. The association 1 country = 1 language has never been true.
Nintendo had the same problem with the 3DS: the console only offers videos from the country it was set up with, and this content is geoblocked because distribution rights. When in a foreign country you can't access local videos (not in the menu) nor home videos (geoblocked). Being a migrant I raised the issue to customer support, which told me it was unfortunate but I was such a special case they wouldn't bother modify their system for me. Guess when it was solved? The following summer, when presumably the execs from NoE and their family went on vacation in southern France or on the coasts of Spain and their kids would not be able to access Nintendo videos on their 3DS. Angry calls must have been made.