It took me a week or more to download the complete 16 million tweets.
Another problem with the corpus is the fact that (at the time I downloaded the tweets) around 2% of the tweets in the corpus were no longer available from twitter as users deleted their twitter account. The longer you wait, the more tweets are going to be unavailable.
Because of that, I do not see how anybody can even think about using this dataset for research.
If you keep all data, you are in breach of the license. If you do not, you are guaranteeing that you cannot reproduce your results in the future.
Als, there is the practical side. I would guess it takes a week to check for deleted tweets, too, so how are you going to comply with that clause?