It's not really a hedge. A hedge would be something with an inverse correlation -- so when the stock went down, your borrowing income would go up. In general, the opposite is the case: if the stock goes down, but the borrowing cost is the same in percentage terms, your borrowing income goes down. The exception is if the stock goes down and demand for shorting goes up so fast that the interest rate on borrowed stock goes up. Even then, it will almost certainly be a small cushion (losing 49% instead of 50%) not a hedge.

That said, it's still income you wouldn't otherwise have.