I believe you can. Each of these pseudo-slot machines are statistically independent and have finite variance; the law of averages applies. It's very different from the chaos situation you have in predicting the weather, which is sort of like trying to play a pinball game twice exactly the same way. You can't play the exact same game of pinball twice, but if you had a million pinball players, you could calculate the average score across players very accurately.  If you had a million slot machines being used 24x7, you could calculate your income very accurately.

In fact, the bitcoin algorithm itself depends on being able to predict the total rate of increase of bitcoins, so it has to be possible.