Of course it's possible; emulators are always reading native game code and translating it into something your computer can process. I know what you're talking about in regards to jailbroken iOS devices; my iPod Touch has GBC A.D. on it, and there are achievements for specific games. From what I gather, emulators need to have very thorough idea of what the game is doing in order to do this. This is something that would have to be done by human observation first, then implemented in an emulator.
For example, say you had a Tetris game you wanted to set an achievement for, like getting 50,000 points. You'd run the game through a debugger, look at the assembly to see where the code updates the score, then code the emulator to set the achievement when these conditions are met. Ideally, if you're making achievements, you should have a good understanding of the native game code, or at least the parts relevant to the achievement.
This can be pretty time consuming, so it's not likely to implemented in Dolphin soon (or at all). There's nothing stopping any interested hacker in doing this himself/herself. If you did want to help, the obvious thing to do is to start learning programming (preferably in a high-level language first), then school yourself in the GC/Wii's PPC assembly. That's what I'd do at least. Easier said than done, however :p
For example, say you had a Tetris game you wanted to set an achievement for, like getting 50,000 points. You'd run the game through a debugger, look at the assembly to see where the code updates the score, then code the emulator to set the achievement when these conditions are met. Ideally, if you're making achievements, you should have a good understanding of the native game code, or at least the parts relevant to the achievement.
This can be pretty time consuming, so it's not likely to implemented in Dolphin soon (or at all). There's nothing stopping any interested hacker in doing this himself/herself. If you did want to help, the obvious thing to do is to start learning programming (preferably in a high-level language first), then school yourself in the GC/Wii's PPC assembly. That's what I'd do at least. Easier said than done, however :p