Short version. As noted 3ds stuff can trick a viewport into rendering wider hence widescreen patches. Some consider it distinct from increased resolution but it is still a type.
If you saw some of the things done for various modded versions of emulators and more recently incorporated into mainline desmume then in hardware it is not a universal thing.
Your options for doing anything in hardware then somewhat mirror the options you have for speeding up a game, and incur about as much difficulty. One day an additional hardware mod might be achieved but that is not likely in the next decade outside of some university student having a silly project.
Anyway some games will decrease the effective resolution like it is 1995 and we are trying to play Doom et al on an ageing 386. The hacker, likely a cost to framerate, could increase things in these instances. The DS does not really have a major resolution modes for its 3d aspect like some older consoles which might vary between menu and in game. Whether you could counteract some negative effects by bringing fog further in and reducing negative effects is going to be more subjective.
Microscopy notes the difference between resolution and apparent resolution. I once had a discussion on how it might be possible to take I think it was a copy of the player model from a Kingdom Hearts sequel and backport it to the first DS game, such a thing, as well as more creative traditional editing of things*. Similar would apply to textures and adding those on to things that might be material (which did include vertex colours as part of it rather than kicking to to textures). You might also fiddle with camera placement to achieve something similar (a far easier task, see some of the stuff done for first person pokemon).
*if you are at all familiar then do be aware that especially with the low poly counts of most DS models that subsurf is not going to do much good.