If you are talking about getting event Pokemon, then no. For starters, the events for Emerald were only available in real life using infrared as the DS didn't exist at the time and there was no wifi on the GBA.
So the only way to get an event like that was to go to an official place where they were distributing the Pokemon locally. Of course, Nintendo aren't doing those events any more (Emerald was years ago!)
But this wouldn't work on a DS game (like Diamond) either, because the events do not depend on your local clock, they contact a server online to get the Pokemon. If the server has stopped doing the event then you just get nothing.
I don't know if there were any other type of events actually programmed into the game. If there were then it may be possible, otherwise no. For example the "diamond dust" weather may have been visible on some dates. But as far as I know there weren't any good events programmed into the game itself.