The guy who made the Mario World and Mario 2 palette restoration hacks (Asaki) did look at and play around with Yoshi's Island, but he said it was going to take more time and effort than the previous two. He hasn't posted in years and he seems to have disappeared from the internet since releasing the Mario 2 hack. He also released a palette restoration for Breath of Fire GBA, but I lost it in a hard drive crash (and I can't find any working links online anymore either).
I did find another preliminary attempt to restore the SNES palette, but it hasn't been continued since 2011 apparently and only restores a small part of the beginning of the game I think-http://www.smwcentral.net/?p=files&u=12961
The GBA port of Yoshi's Island is a mess. Besides palette and sound downgrades, there's slowdown at times. The palette i imagine is fixable. And I suppose it's possible to correct the sound issues, Bregalad fixed the Final Fantasy ports and released tools and documentation on GBA sound. His hacks even fixed a lot of the slowdown in FF5/6, so the same might even be possible for YI. Most SNES to GBA ports suffer from brightness, sound and slowdown problems. Likely could have been avoided with better programming too.
Even with SuperFX, GBA should have a power advantage. Plenty of impressive original GBA games to showcase its power. It's a more capable 3D machine and can handle sprite rotation/scaling on its own (SNES required SuperFX for this). Gunstar Super Heroes in particular is full of this. Bregalad's hacks even showcase faithfully replicated SNES music/sfx on GBA.
I'm definitely not a programmer and don't claim knowledge of technical matters, but I would think that (based on other games) the GBA should be capable either of the Touch Fuzzy Get Dizzy distortion effects, or at least a reasonable facsimile... There are actually original Gameboy (black and white) games that use very visually comparable distortion effects. Here's an example from Link's Awakening-https://www.youtube.com/watch?v=geikcS9wb90&feature=youtu.be&t=371
Some of the battle backgrounds in Earthbound also use distortion effects that look similar to the Fuzzy effects (particularly the final battle), left intact in the GBA port.
Again, I don't know for certain if the exact Fuzzy effect could be replicated 100% on GBA, but i've seen more than enough from other games on GB and GBA to convince me that at the very least a reasonable facsimile could have been used to approximate the effect
The only thing that i'm unsure GBA is capable of are the "dripping" effects from Kamek's magic. It's a curtain of transparent color (with a gradient shade) that pours over the screen, and it stretches vertically in places. Though I will also point out that the Sluggy and Potted Ghost bosses look like they use some variation of this exact effect (at least similar visually), and those effects are intact in the GBA port.