Gamecube had pretty low power draw, so if it was limited to 10W, technically it could've been viable option for Switch like portable.
That said, batteries of that period would be huge problem - you could either go with Li-Ion, which were cylindrical, so you would probably need to put them inside handgrips, like in Ally ROG or MSI Claw (so forget about Joy-Cons), or go with, back then, very new and expensive Li-Po batteries that could be shaped to fit inside device.
Again, all that would cost arm and a leg.







