I can't really answer to "Yes" or "No" because after you create that household by CAS story mode, save the household and reload, the story element no longer exists on the character, so you are stuck with the base §20,000 add the usual §2,000 per head isn't counted either. so trying to create something with that is very tight for 4 sims in a household. However any jobs assigned to those characters remain within 2 or 3 ranks and some of those in the household end up lacking in skills where others have all they need to promote.
it is rather hit and miss so far with CAS story mode at this point.