Maybe to some countries it is like that but here, for Premier League teams, Club over country, every single day of the year. Well for a lot of people anyways.
We pay his wages, including when he will be away with Australia. When we signed him Australia were still in the Oceania area so it wasn't an issue for us. We pay the price because a country decides to change federations, when it wasn't even expected? Why should we lose one of our key players at THE most hectic time of the year, where we play some massive games (the derby being one) in a very short space of time - a time when you need to use your whole squad. We've let Tim go whenever he has wanted (including inconvienient times for us), when it didn't suit us. I know he wants to play for Australia but we are his bread and butter, we pay his wages and we gave him his break in the top league.
What if we had an injury crisis then (not impossible with us)? I'd trust him to make the right decision if it got to that point. (Maybe "right decision" isn't the correct term, more a decision that would help the people who pay him.)
The European Championship is different as not many European internationals play outside of Europe and most European seasons run in situ (thus the tournament is out of season).
All in all, I expect him to go though, because we are a club who cares for their players and their feelings.