Tweets seem to have an impact of around 1-3% lasting hours to days. Many (most?) stocks have too high implied volatility to begin with for straddling by tweet to be a productive strategy.
Even as an ensemble?
If you could spot the tweet and know the direction it'd move there might be cheap enough options to make money on one side, but the "ensemble" aspect of a straddle means that you need to make twice as much to cover the premiums before you make any returns.