The wii u is fully compatible with the Gamecube at a hardware level thanks to the wii chipset and you can play Gamecube games if you have homebrew installed and nintendont but they never released VC Gamecube games for wii u.
Running gamecube games on the Switch under emulation seems unlikely. They will probably just use the graphic assets and have the main game code recompiled for arm. The nvidia shield struggled a bit emulating gamecube and that uses the full Tegra X1 chipset at a 2ghz speed for the 8 cpu's. Not the likely 1ghz quad core arrangement of the Switch. In theory the Shield could be up to 55,200 mips compared to 18,400 for Switch. So about a 1/3 of the cpu performance. Saying that we don't know what customisation has been added by Nintendo maybe there is something interesting in there. There was no indication that the Switch dev kit had anything other than a cutdown Tegra x1 though.
