Only if they actually carry over the games to the next system, which I don't think will happen.
Nintendo's interest in providing legacy content to their player base is so low that it's somewhat surprising that Genesis, GB/GBC, and GBA games were added. NES, SNES, and N64 seemed like a given from pretty early on.
GameCube and Wii games are recent and "modern" enough that Nintendo would likely rather port, remaster, or remake them than allow us subscription access to them.
I don't see any GameCube or Wii games coming to the Switch unless they are sold on the eShop (like I just mentioned). I could easily see Nintendo charging $20-$30 for ports of GameCube and Wii games, and they've shown $40-$60 is their desired price for remasters and occasional remakes.
Switch 2 (or whatever the next platform is) may have GameCube and Wii games added as part of a subscription, but I'm not counting on it.
Interesting enough, the most likely platform that could be added to Switch (but probably won't) is the PC Engine/TurboGrafx-16.
Lifetime Sales Predictions
Switch: 156 million (was 73, then 96, then 113 million, then 125 million, then 144 million, then 151 million)
PS5: 115 million (was 105 million) Xbox Series S/X: 48 million (was 60 million, then 67 million, then 57 million)
PS4: 120 mil (was 100 then 130 million, then 122 million) Xbox One: 51 mil (was 50 then 55 mil)
3DS: 75.5 mil (was 73, then 77 million)
"Let go your earthly tether, enter the void, empty and become wind." - Guru Laghima
