No.

So, just because you file for legal divorce because of the domestic violence doesn't mean that the divorce has happened Islamically.

Either the husband has to pronounce talaq, or has to agree to the khula, or you have to go through the faskh process.

Some scholars will say that the man signing a settlement agreement that says that I agree for the divorce may count as a divorce. But there has to be some type of acceptance by the husband or some type of islamic court order that dissolves the marriage