Garmin supposedly does this with their 760,770 and newer gps... For an added fee of course. You run a Garmin weather app on your smartphone and that links with the GPS unit, or something like that.
Tornado spotting is very last minute, I wouldn't count on anything but a weather radio or cellular emergency alert for something like that.
Thunderstorms are pretty reliably forecast, not sure how you get surprised by one? Review the daily forecast for areas along your route on weather.gov before setting out in the morning.