Not for me it didn't. I initially "reset all settings", which of course loses all folders. Since I have more apps than the maximum number of allowed screens, I had to reorganize the first group of apps back into folders, then respring the phone to make the second half show up. Sure enough, the last icon on the last screen was the white "springboard" one, still there despite the reset.
I then tried a full restore from backup. No luck: the Springboard icon had been saved in the backup file. It was also in the prior one.
So, while the "reset all settings" approach does seem to work for some, it doesn't work for all. If it doesn't, the only way to get rid of the problem is a "greefield" restore.