Well, I haven't exactly done a lot of work with changing the day other than continually setting it back one day for a while so I could continue to chain Absols while they were swarming. So it is possible to repeat events/adjust the clock, although you do have to be careful about how you do it--certain things don't register as forcing the game into a new day. Again, it's been a while, so I don't remember exactly what it was that didn't work, but yeah. If I can remember, I'll reply again and try to be a little more helpful/specific.
I also believe that simply removing the game from the DS will halt any timed events until you put the game back in, as it won't have the clock to keep track of anything. That may or may not be useful to you.
The one thing you do need to keep in mind is that adjusting the clock, even if it's just for daylight savings time, will prevent you from using the Pal Park feature for the next 24 hours. This is because you're only allowed to park Pokémon in from any one GBA game once per 24-hour period, and they don't want you adjusting the clock to cheat that limit. So if you're going to fiddle with the clock, don't do it around any time you're anticipating needing Pal Park. And when you do adjust the clock, you should immediately try to use the migration feature anyway. The game imposes the 24-hour wait as soon as you try to use the feature, so you should go ahead and get it started as soon as possible; otherwise you might have to wait for the 24 hours to be up at a later, less convenient time.
Granted, if you've only just started then you won't have that option available to you yet anyway, but it's worth keeping in mind for the future.
...I feel as though that was horribly unclear, so if it was then please tell me and I'll try to clarify.