Using training data generated with pure regular expressions - Can machine learning surpass the accuracy of your regular expression?
No- not if your regex is actually generating the data. If this is the case, the regex (or a complementary one) should be able to classify the resulting text perfectly. That is, you know what the rules for creating a 'happy' or 'sad' piece of text are within the regex, and so you simply apply those rules backwards to classify it. 

So, if you take what the regex says when it creates the data as ground truth, then there's no reason to create a machine learning classifier to classify it- the creation mechanism itself already does so.

On the other hand, if you have created a regex that will produce "happy" or "sad" tweets, and you want to know if the regex itself or a machine learning algorithm will better conform to the opinions of, say, human observers, you would have a very interesting question to evaluate and a relatively straightforward test case for sentiment analysis.