RAI? Probably not.
RAW? Probably. This is more of a philosophical question, and based on the convention of using "nothing" and "0" with the same meaning.
A similar case: A man is asked to give all of his money to his neighbour. The man has no money, but "nothing" can also be measured as "0" (since that's what his bank account says).
- On the one hand, he CAN'T give any money, since he has none (no CHA mod bonus allowed).
- On the other hand, he has ALREADY fulfilled the requirement of giving an amount of money equal to his total owned amount away, since he has given no money at all (CHA bonus allowed).
So it's really up to the DM until we get an official FAQ-ish answer based on the intention behind the feat.