Ok, I tried it with my 3DS and my XL. Answer is definitely no. You have two different options for multiplayer with multiple cards and multiplayer with only one, but the options afterwards are exactly the same. That being said, all consoles have to be updated with the latest firmware (V 4.5.0-10E in Europe), to be able to play.
Also, the people DLing the game can continue playing after the host quitted, can quit the game and even go play online with friends (or the rest of the world), or create another local game to play with people that have it or that have DL the multiplayer demo.
Wow, I'm just discovering that and... Nintendo as done an *awesome* job with their multiplayer, as far as one card play is concerned !!
tl/dr : Once you have DLed the game with DL mode, you can play the totality of the multiplayer, as long as you don't quit the game. The only thing you can't do is allow other people to DL it if you don't have the card, which is common sense.