the biggest problem with online tournaments would simply be the amount of time it would take to implement, not to mention that, unlike REAL tournaments, there'd be no payout. As much as you may dislike it, all regular tournaments ARE usually held for a pot (especially MLG sanctioned ones like Super Champ Combo) and it'd be literally impossible for that to work.
In terms of smaller, 'just for fun' tournaments, that'd be down on the respective members trying to hold it to get it to work. But remember what you're saying:
--First, you need to make brackets.
--Then, you need to make sure everyone has each other's friend codes.
--Then you have to have some way to officiate EACH and EVERY match- that means at least one judge per match (as someone earlier suggested, possibly two, but that would be even more tedious, since you'd need twice as many judges)
This may not sound like a lot, but I've held wifi tournaments for DS games myself, and I can tell you that even a simpler tournament format like round robin (running under the honor system, mind you, meaning NO judges) can take in excess of 6 hours. Co-ordinating many people over the internet to play each other, and making sure each of their matches gets a judge in it, would be very time consuming, and most people would have neither the time nor the patience to put up with something like that.
Is it impossible? No. But impractical? Very much so, especially considering it'd just be for fun.
Now, if you did round robin under the honor system (I would hope that, with no pot on the line, smashers would have a bit of integrity) then a tournament could probably go a lot more smoothly. Actually, under the honor system, even brackets would be possible if the turnout was too big for round robin.
Regardless, if you wish to undertake that difficult process when Brawl finally releases, I wish you good luck and hope that things go as smoothly as possible.