It should work if you buy it via Xbox (the DLC is listed separately there) then go to the Switch if both are under the same Microsoft account. I had this happen in the past with various packs.
That said, I don’t know if it will work with a direct purchase and not a coin purchase. Mostly because I wasn’t aware until now you can buy packs separately on Xbox.
Edit: To answer your other question, it’s not good. Laggy at the best of times, with long loading times, plus needing multiple NSO subs to play local multiplayer.