This probably won't happen. Even the 3DS doesn't have enough power to run N64 games fullspeed, not with homebrew anyway. Nintendo might be able to make a fullspeed emulator since they have a large team, infinite money (for that purpose anyway, it's not like it would ever cost them a large part of their money), and know all the specifications required.
However, the DSTWO being 400mhz compared to the PSP's 2x333 mhz (and the losses in power due to having to synchronize the 2 cores, which the Daedalusx64 team said was about a 30% loss at best, if it was fully optimized) means the PSP is technically only slightly more powerful for N64 emulation, so the DSTWO could potentially run N64 games almost as well, but even Daedalusx64 doesn't run N64 games terribly well, most games run at around half of normal speed (unless they have made huge improvements since last I tried it, but I don't think there is much more they can do to improve speed)
I doubt anyone will spend that much effort on porting or coding an emulator knowing that it will never run anything at full speed though, but some may consider 30 FPS to be fully playable. I don't though, as it ruins the audio and that is a big part of any game to me. But audio might not be implemented in an emulator anyway if one was ported.
However, the most important factor to consider is that there are far less DSTWO owners than PSP owners (and far less developer interest), which makes this very unlikely to happen. There is only a handful of DSTWO homebrew compared to the huge pile of PSP homebrew, and it takes someone highly skilled (and highly knowledgeable in how the CPU architectures work) to optimize an emulator to the level that it can actually run games at a reasonable speed.
The DSTWO could potentially run N64 games almost as well as the PSP (read above), but even the PSP doesn't run them that well. And as there are far less DSTWO owners than PSP owners (and far less developer interest), this is very unlikely to happen.
However, the DSTWO being 400mhz compared to the PSP's 2x333 mhz (and the losses in power due to having to synchronize the 2 cores, which the Daedalusx64 team said was about a 30% loss at best, if it was fully optimized) means the PSP is technically only slightly more powerful for N64 emulation, so the DSTWO could potentially run N64 games almost as well, but even Daedalusx64 doesn't run N64 games terribly well, most games run at around half of normal speed (unless they have made huge improvements since last I tried it, but I don't think there is much more they can do to improve speed)
I doubt anyone will spend that much effort on porting or coding an emulator knowing that it will never run anything at full speed though, but some may consider 30 FPS to be fully playable. I don't though, as it ruins the audio and that is a big part of any game to me. But audio might not be implemented in an emulator anyway if one was ported.
However, the most important factor to consider is that there are far less DSTWO owners than PSP owners (and far less developer interest), which makes this very unlikely to happen. There is only a handful of DSTWO homebrew compared to the huge pile of PSP homebrew, and it takes someone highly skilled (and highly knowledgeable in how the CPU architectures work) to optimize an emulator to the level that it can actually run games at a reasonable speed.
It worked in DSi-mode on the 3DS. There was just no way to switch it to DSi-mode since it didn't work in DS-mode. If they hadn't abandoned it, it could still be working in DSi-mode on the 3DS, so it's a sad thing that they did.The PSP is much more powerful than the DS.
It doesn't matter if a flash cart runs on the DSi or 3DS, they only have access to the power of the original 2004-model DS.
The iEvo is an exception, but it's only double the DS's power (which is still crappy), and it hasn't been updated in ages (and didn't work in DSi-mode on the 3DS anyways).
The DSTWO could potentially run N64 games almost as well as the PSP (read above), but even the PSP doesn't run them that well. And as there are far less DSTWO owners than PSP owners (and far less developer interest), this is very unlikely to happen.