Hey Mimi!
It's recommended that you submit a Rich/Influential application and EFB before you begin extensive work on the character. I might say you could work out an outline, or work on things not having to do with their history, but these statuses tend to affect pretty much every aspect of a character's life so it's wise to wait on the Administration's decision on the application for the Rich status before you move forward with character creation.
And yes, you are correct. Non-pureblood lines do not require EFBs unless they are also Rich or Influential families.
Hope this helps,
[ash]~ Ashton[/ash]