So (I don't mean to link to myself here, sorry) this might help answer your question. It has more to do with NNIs than what I think you're looking for, but it should still help somewhat. But here is relevant data to fully answer your question:
- Your Nintendo Network ID is tied to your software and/or additional content you have purchased and downloaded. (Meaning if you have an NNI, the purchases you make are not linked to your console, but your NNI)
- What is retained (when you create a new NNI): All game licenses purchased prior to linking a Nintendo Network ID, funds added prior to linking a Nintendo Network ID, and all free software demos downloaded prior to linking a Nintendo Network ID. (Just proof that anything that you download with an NNI on your system is retained)
Recently I bought the Persona Q 3DS and transferred data from my 3DS to the Persona 3DS. When I transferred my data, everything I bought moved from my original system to the new system. But the reformatting process will remove anything on the target system having to do with another NNI. But... no NNI is technically ANOTHER NNI so... You say your games (on one system) aren't connected to another NNI, but if I were you I would back those up just in case.