It does remain along with the hacked save after doing a recovery update. Even low firmware downgrades like 9.2 to 2.1 or 11.0 to 2.1 along with recovery to 11.0 works.
Source: I downgraded a o3ds twice from 11.0 to 9.2 to 2.1 and ended up semi bricking both times. The fix was to recover to 11.0 (and try again)
I did solve it by going directly from 11.0 to 2.1, skipping 9.2