I could easily see birthdays; their celebration is pretty universal.
Christmas is a bit less palatable, not because of Japan's Shinto majority - they still have a very bustling Christmas season - but rather I could see that raising red flags from other religions. Will the Jews want them to include Chanukah? How about the Muslims expecting Ramadan? It's a neat idea but I don't see it happening because of this worrying complication.
National holidays are also not so feasible considering that this game is released internationally: I don't think they'll want to program that barrage of American flags on the fourth of July only for the American version while relegating all the Dutch celebrations on the 30th of April. But more importantly, Shinou is not a part of the United States/the Netherlands/Germany/Japan/etc. There is no reason to include national holidays for real nations...
...however, in lieu of that, they could implement festivities that pertain to the Pokemon world. They would be rather arbitrary and spaced pretty evenly in the year. For example, Shinou's national holiday could be the 10th of August, when the professor in the game defeated the President of the Pokemon League with his team of all-star Pokemon, allowing Shinou a greater degree of autonomy from its corrupt regime. In addition, the day you become a champion could be labelled Ascension Day, and on that day every subsequent year, you would be offered a challenge by the former/current Champion with his best team of Pokemon, all level 100 and EV trained.
Real-life holidays are too far, but it can't hurt to give the Pokemon games a sense of culture by alloting them their own holidays. Though, I would suspect that most would be monthly or something; a year seems a bit too long to wait for a recurring event.