so we have:
The sims 1 console (2002)
The sims 2 console (2005)
the sims urbz (2004)
the sims bustin out (2003)
the sims 2 pets console (2006)
and finally the sims 2 castaway console (2007)

there has been various emulator mods for ps2 and GameCube games on emulators, Yes You can still used gamesharks or action replay, but emulator hacks take a step further by Being able to do things that you couldn't do originally in the game

could it be possible to mod the said console games listed above?

Yes it is possible. One of the easiest things to mod is textures. Using PCSX2 2.6 (or higher) you can enable texture dumping which will let the emulator dump texture files from VRAM into a .png file on your disk. You can then replace the textures with your own. However PlayStation 2 textures tend to be partially transparent due to the PS2 supporting a transparency method not utilized on the other consoles of its era. So if you want to replace the PS2 textures you'll need to know how to set them up so that they're properly rendered in the emulation. You'll also want to make sure the file names are the same exact as the original dumped files otherwise they will not load into the emulator. PCSX2 in that regard is different than it's cousin, the PlayStation 1 (PSX) emulator "DuckStation" which has the same texture dumping and replacement method as PCSX2 does but allows you to name your replacements provided they still have the original memory address in the beginning of the file name.

Keeping in mind that large textures will reduce performance in the emulation worse than native PC games. So use caution when replacing.

And if you're wondering, yes it is also possible to extract meshes and sound files from PS2 ROMs, but IIRC there is no easy way to replace at runtime in the emulator, and you'll instead need to make an entirely new disc image (.ISO) file.

My knowledge is only with PS2 emulation as I rarely play GameCube games, outside of a few select exclusives. My experience with Dolphin emulator is very limited, but from past attempts I do know that emulator does support texture replacing, but how you would set that up and what file types are needed is beyond me, since again, limited experience.

Currently, I've been modding Bustin' Out and The Sims 2 (original, not pets) textures. These console games have a lot of unique floor and wall textures that I have been upscaling, replacing, and even porting over to my PC TS2 install.