Yes, very practical.
Character N-grams have known a priori distributions, among other clues. For example, a listener could probably manually pick out the periods and space characters of a passage of natural language, even without a computer.
An automated system could do even better.
You have one parameterized system working to categorize the clicks, with some pretty good initial guess using, e.g. PCA.
You also also inferring a categorized-click-to-character map which minimizes the difference between observed click-N-grams frequencies and a priori character-N-gram frequencies. You could approach the problem with simulated annealing, with the click-to-character map (and the click-categorizer parameters) as the solution space and let the evaluation function be a function of the N-gram distribution differences.
Note the method is very tolerant of noise - e.g., even if some clicks are not being completely distinguished from each other you'll have some idea about which characters-clicks are close to each other. That will help in making password guesses. A lack of known click-to-character key training data is not going to be a limiting factor.
In my judgement, this is a real security issue, mostly because cell phones are easily hacked. A noisy keyboard and a single passage of say one thousand words worth of natural language typing noises would be enough to start making educated guesses about passwords.
Also, testing random key pairs on my own keyboard right now pretty much every pair can be be distinguished.