Not in the same way you might see various 3d based systems do it wherein overlays (usually UI or some kind of shadow effect) and the odd bit of logic or whatever viewport rendering/backface culling are the main things to cause the would be widescreen/resolution bump mod some fun.
Everything in the GBA hardware (and barring some truly exotic thing then every primarily 2d console I have ever looked at*, which is most of them at this point) when it comes to graphics is based around the size of the screenhttp://problemkaputt.de/gbatek.htm#lcdiobgscrollinghttps://web.archive.org/web/20120622062908/http://www.coranac.com/tonc/text/video.htmhttps://www.cs.rit.edu/~tjh8300/CowBite/CowBiteSpec.htm#Graphics%20Hardware%20Overview
The next pixels might exist in some hypothetical state so it can display them quickly next move, and some things off screen might similarly be present but not displayed. However so much code revolves around it that it is not worth it (you can see it in various BG/map viewers in emulators).
That then leaves the pause every frame, walk each direction (or figure out the camera thing for that game and force render) and stitch it together before returning control back to the frame as it started option and I am not sure what goes for this one these days (I have seen some do something for some systems). You also then hope no random battles get triggered (or the emulator knows enough to sort it) or other things that trouble the screen. Also hope no animations get rumbled this way -- my usual suggestion is the scrolling stars background in various tetris worlds menus as it is just a slightly larger bitmap (some modes do have more space) that it moves around in a set pattern, though the pulsing glow of summon night save swords is not a bad one either.
*for 2d stuff then some PC things will use some more abstract world setups where you could bump it over into that and possibly some 360/ps3 era stuff for 2d but I have not pulled apart those so much. PS1 2d games could also possibly have something but its widescreen hacks are already a world unto themselves compared to most others so yeah.
Short version. Better hope there is a remake on something later and more amenable to hacks or someone willing to help you recreate some source code. I guess you could go nuts and go game by game to figure out what makes for such a hack (no random battles, how to decouple camera from collisions, possibly some sprite aware stuff if you would rather not have the random moving NPC clone themselves and split off in some kind of parallel timeline all displayed at the edge of your vision) that makes the savestate and move the camera before stitching it together bit that bit better than the basic setup that just needs a bit of computing grunt to pull off.