People have broken sway bar brackets when autocrossing their Miata with the big Racing Beat tubular bars and stock springs. With stiffer aftermarket springs + no autocross, I agree with James that you won't be breaking anything. If you're worried though there are HD mounts that you can buy.
Due to improper installation, yes people have broken sway bar brackets. If you install them correctly, you won't have any problem. I've had the big sway bar on mine for what? almost 6 years now? And the car was / is used nearly exclusively for motorsports... currently on pretty huge slicks (first event with the slicks, the VLSD pooped the bed...). Never bent or broken a stock suspension component though.