Topic: does the sd card get corrupted if its removed while the new 3DS is on?

I'm wondering if the new 3ds just remains in the main menu and if the micro sd card was just inserted with no changes made to it, would it say that the card is corrupted or something like that? Like I don't know whether I did it or not because I don't know whether it was before or after I turned on the N3DS XL that I removed the card. So far, nothing seems to happen as I successfully downloaded majora's mask update with no issues........

There's a chance it might but that's with any product that you remove an SD card from while it's on, hence why it's not recommended to do so.

even if its in sleep mode?

I suggest you don't try it. Make sure it's completely off. Unless the user manual explicitly states that Hot swapping is allowed, don't try it. Sure it could work the first couple times. It may never fail, but do you really want to risk it? Games can always be downloaded. Save data, not so much.

Sleep mode isn't off now is it. Sleep mode is a low power state not off. The safest thing to do is to turn it off completely before removing it.