you'll definitely be fine in that regard. i think the 3rd party adaptor and official adaptor are doing the exact same thing, so it would be a lot of work on nintendos part to try and exclude the 3rd party adaptor from working, while also ensuring their own adaptor works, while also ensuring all currently Nintendo licensed 3rd party products also work. i just don't see it happening!

quality is more of a concern in terms of the 3rd party. i got mine (3rd Party gamecube adapter) when smash came out on wii u. the slots were a little tough and would make plugging and unplugging controllers a bit difficult. i've used it many times though in the past couple years and it's never not worked. always worked totally fine.