Will I keep the progress for my 3DS games if I delete my Nintendo Network ID?
Solution 1:
According to Nintendo, game save data is saved directly to the physical game cartridge. So, deleting anything on your 3DS shouldn't affect the save data stored in the cartridges.
There seems to be some rare exceptions to this rule -- e.g. Super Mario Maker saving both to cartridge and SD card -- but you should be fine deleting your NNID without losing progress data :)
Note: it looks like Pokébank is linked to your NNID, so you may lose any Pokémon you have in the Bank.