In a neutralization reaction between a strong acid and weak base, can I assume the weak base is totally ionized?
You're never going to puzzle this out without some guidance so here goes...


  Why, if it is at all, correct to assume all of the base reacts?


All of the base will never react no matter how much acid you add. If you setup the equilibrium equation you can solve for $\ce{[NH3]}$ for any given pH. Thus there will always be some small amount of $\ce{NH3}$ in an acidic solution. 

The gist is that there is $5.70\cdot10^{-4}$ moles of base. If you add "exactly" that much acid then the necessary assumption is that the acid balances the base and the solution is neutralized. 

One other thing to consider in all of this is the significant figures. So +/- $1\cdot10^{-6}$ moles of acid doesn't make any real difference. That is enough to swing the final pH from 6 to 8. 

Just like for the acid if $\ce{[NH3]} &lt; 1\cdot10^{-6} $ then the free ammonia is negligible to the amount of $\ce{[NH4+]}$. Thus, considering the significant figures, the assumption that all of the ammonia was converted is reasonable, even though it is not actually absolutely true.