For the case mod, they may fix it (the DS) for a cost, or would simply ship it back.
The flashcart would be put aside, and sent back with your DS with absolutely no attention paid to it.
Flashcarts are legal. They enable the use of homebrew apps, and aren't technically illegal. As well, they wouldn't scavenge it for pirated games. They don't care enough to do that.
I assume they don't think suing/charging little 9 year old Billy for having a flashcart and pirated games would be all that worth their time and loss of reputation.