While I I don't doubt that there will be many uses for machine learning algorithms and natural language processing in the future, from a physical science POV I don't see the computer algorithms replacing radiologists (or any doctor for that matter) - within our lifetimes.
From my understanding of the methods used in these algorithms is that they're using statistical methods, as precisely solving Baynesian integrals with non-trivial amounts of realistic real world parameters would take a long (or perhaps infinite) amount of time. Therefore, mathematically there will always be an error function (these computer algorithms are based on
statistical inferences) which is represented here:
http://en.wikipedia.org/wiki/Bias–variance_tradeoff
This error can't be overcome by simply expanding the data set, i.e. the difference in having 100,000,000 data points and 10*10^(10000) data points would result in infinitesimal increases in accuracy: as described by Baye's limit in statistical mathematical inferences.
http://en.wikipedia.org/wiki/Bayes_error_rate
(Which, btw, even in mathematical theory isn't fully well known or characterized at this time in 2014)
So the question then becomes, with assumed infinitely large data sets, can the "best" algorithm outperform what is serviced today. I.E. doctors. Can their minimum mathematically conceded error rate be lower than a doctor's? And even if it could, would we as humans be willing to trust a computer with a known error rate? This is an interesting question and one that I believe is no. The amount of parameters that need to be evaluated in making a clinical decision is very high, and the curse of dimensionality ensues that would probably take a computer an infinite amount of time to solve, even with lower dimensional manifolds and other simplifying model techniques.
As an aside you always have the problem of emerging health epidemics - new influxes of disease into the human population where existing data would be scarce and the computer algorithms would be useless.
Although I am by no means an expert PhD in computer science, so I might be missing something, and would welcome someone chiming in, but in my view the answer is no - or at the least - not within our lifetime. As an example, computer EKG interpretation algorithms are still not better than non expert clinicians (probably due to trying to recognize highly non-linear patterns of EKG - which is computationally intractable or would take an infinite amount of time to solve.)
http://www.sciencedirect.com/science/article/pii/S0022073611001622
And that's probably one of the areas that's most prone to automation. I would say I would be more worried if they figure out EKG interpretations. That would be step 1