Through testing so far, it appears you can post replays for anyone in the world to see immediately, but sending a replay to friends only means they can't see it for quite some time. Logical? Guessing it has to be sent through other online features, and Nintendo even says it might take a while. Better to just post them.
Another fun thing: you can now search for replays others post featuring you. Just search for your main and the mode of play, and scroll through the list looking for your name. Myself, I posted a replay with leito, myself (as P2), kam, and "....". Two posts above, I found myself in an earlier match with a different P4 who left after two or three matches, and posted the earlier replay. You'll find both under Team Smash For Glory by focusing on Kirby.