This simply isn't right. The problem is not the game, there isn't anything to reprogram. Otherwise the game would have lag problems with Dolphin. The lag is caused by the necessary processing of a standard definition image on a HDTV.
- GC converts the rendered image from digital to analog, typically interlaced due to the rarity of component cables.
- TV receives the signal but has to covert the signal back to digital
- TV now has a picture, but it has to deinterlace it.
- Now the TV has a usable picture, but the resolution doesn't match the TV's display resolution, so it has to upscale.
- Finally, the TV does its image quality processing (varies depending on the TV and video settings) and displays the picture.
Switch would eliminate most of those steps, though it will vary depending on how it handles GC games. If it renders the game at 720p or 1080p, it would skip everything except step 5. If it renders at the original resolution, it would need to do step 4 either on the console on the TV. Likely the console based on Wii U (Wii games are upscaled by the console), but the console or a sufficient monitor would work.
For what it's worth, a Wii + Sewell HDMI adapter + good low latency gaming monitor has less than 1 frame of lag and is for all intents and purposes equal to a CRT. I think LucidMomentum uses setups like that at his locals, and I use that myself. A VC release would have even fewer conversions, so it would be even better.