OK, just read up on that, interesting that the US itself made that decision. But if the US wants to call on NATO for help, NATO will agree to that I think. Now, not every nation might sent a ton of troops or go all out war. But to ignore the US request at that time would mean a breakdown of the alliance and European countries are not going to do that with Russia acting up lately.
Whether the US wants to call upon NATO is a different story of course, they probably won't and deal with it themselves with their Pacific partners.
But European involvement in Korea is not really new, multiple countries were involved in the Korean War there.