I'm guessing he's asking "If you take a backup of the relevant files (those pertaining to console ID and NNID, presumably) before you're banned, then restore them after you've been banned, will this get around the ban?"
Nah, you'd be restoring the state of your 3DS, but your friend code, friend code seed, etc would be the same. Nintendo servers are storing those values and checking them when you connect. Although, it's my understanding though that without a NNID set, you can't be banned, so I don't know. (I'm not even sure you can play online without an NNID set though? Gosh, I've been away a while.)
My hypothesis: Even if you were to restore this blank state, it'll use the same seeds to generate a new friendcode, and you'll definitely have the same console ID.
My conjecture: Nintendo's method of using tickets stored on the client device to verify permissions continues to perplex me, especially when the whole system was blown to bits back when the Wii was cracked open. It wouldn't super surprise me if you could simply *delete* your console ban by restoring those files, but the current method of just stealing another consoles ID, friendcode seed, etc suggests that nah, nintendo is looking at the numbers on this.
