Yes, though -500mV might be a bit on the high side, many chips specify -300mV max. This is more of a practical issue at elevated temperatures, but the abs. max. values typically don't distinguish.
In fact, as @DJNguyen@DKNguyen says, you can buy chips that provide a drop-in solution, such as the LM7705.
I believe Maxim offers a similar part.
