First off, I can't add a huge amount to what Mario has said, but I don't think that this is the sacrificing of good grammar for ease of colloquial expression. It just isn't very good Irish and I am sure that the person who composed it doesn't use Irish on a regular basis. As Mario said, ardú is a verbal noun and the word after it would have to be in the genitive, so it would have to be "ardú na gloine" (the raising of the glass - for reasons of grammar you only put the one "the" in the Irish version). Or you could say "ardaigh an ghloine", which means "raise the glass!" The effect of the phrase "ardú an gloine" is hard to reproduce in English, but it would be something like "raises the glass", because if you saw that on a T-shirt it would just look a bit odd.
However, following on from Mario's comments, I would like to point out that grammar is one thing, and the way language is used in real life is quite another. Let me give you an example. In French, if you say "je suis de trop", it means that you are in the way, or intruding in a situation. The literal meaning of it is that you are too much, or surplus. Now, if you translated that French sentence as "I'm too much" it might be grammatical English, but it doesn't mean what the French sentence means. There's a big difference between "I'll leave you two alone because you obviously have a thing going" (Je suis de trop) and "I'll leave you two alone because I'm unbearably intense and you probably both have a headache listening to me" (I'm too much).
Where am I going with this? Well, the fact is that Irish is very rich in drinking-related terms, and there are lots of ways of talking about drink. You can say caith siar é, ól siar é, preab san ól, bímis ag ól, bíodh cuspa sláinte againn and lots of other things that mean the same as "raise the glass". But I have never heard anyone use the phrase "ardaigh an ghloine", though I have often heard English speakers talk about raising their glasses. So, in other words, this is an English expression that someone has clumsily translated into Irish.
Of course, languages borrow expressions from other languages all the time. This is quite natural and there is nothing wrong with it, but it is up to communities of people or individuals who use Irish on a regular basis to decide what they want to adapt and bring into the language - what works for them and what doesn't. Otherwise you end up with the equivalent of the Japlish you see all over the place in Japan: often grammatically correct (well, sort of) but still raiméis of the first order - "I swing in all my power with comfortable sweat"; "No My Car Day!"; "Puberty Brand Notebooks" (yes, I'm serious) or my personal favourite from an English textbook "She opened up the letter and and found their hot hearts in it". I think I saw that film ... didn't sleep for a week afterwards!
Hope my linguistic rants won't cause you any sleepless nights, anyway.