It's perfectly workable. The bot just needs to weigh its trades properly and provided the sentiment signal has any alpha, it can be combined with other analysis to run a profitable strategy.
I've seen this working and working very well (day job), although not specifically with Trump tweets.
If it works, the last thing you want to do is post it on HN, because it'll stop working once everyone starts using it. Everybody else running the bot will bid up the prices of affected stocks before you can get to it, and so by the time your bot gets around to executing its trade, you'll be buying at inflated prices and lose money as everyone else takes their profits.
Not necessarily. If you can get a bunch of unsophisticated traders on relatively high-latency connections (AKA the readers here) to execute a known strategy, you can actually make a lot of money by simply frontrunning them. :)
I've seen this working and working very well (day job), although not specifically with Trump tweets.