If I sign out of the Nintendo Network ID on my new 3DS XL, will all my downloaded games be deleted even if they are on the SD card?
It depends on how you do it. Ultimately, the 3DS is only designed to have one account assigned to it. If you remove that account, the system will be treated as "new". Ultimately, you will lose access to the games, wither through the format, or though stripped access privileges.
Some people state that the console must be formatted, which will delete all games and data.
go to settings and completely format the system, thats the only way.
However some say that the account can be removed without affecting the downloaded games, by erasing your NNID. However you will lose rights to the games you downloaded (to stop pirating).
the only way possible is by erasing your nintendo network id [...] also you will permanently lose all rights to software titles purchased or downloded in nintendo eshop