Will you get banned for using a flashed or modded xbox 360 to play original games online.?

If you have a flashed or modded xbox 360 and play the downloaded games offline and originals online, will u still get banned on live.

Is it unsafe to play burned wii games online with a soft modded wii?

Okay, so I have a soft modded wii, and I've burned a couple of games for the back up launcher on homebrew.

Say I wanted to play a burned copy of mario kart online with my softmodded wii, is this dangerous? Could nintendo detect my mod and burned game and give me some kind of ban?