"Demonstratable" — a dictionary word, or just a well known hack?

Don't use demonstratable.

The Corpus of Contemporary American English has 262 hits for demonstrable, and none for demonstratable. Google ngram shows a similar result:

Demonstratable is not an English word, so shouldn't be used. People will probably know what you intended, just as they would if you talked about demonstratating the system; but they will never be certain whether you are joking or ignorant.

Demonstratable is recorded in the OED, with examples back to 1814; though it's far less common than demonstrable.

As for whether you'd get away with it in everyday usage, the answer's yes, because -able is a productive suffix in English, at least in informal usage: in other words, you can add '-able' to lots of verbs and create adjectives with the sense 'capable of being [x]-ed'.

The note attached on MW is to say that access to a word in their full dictionary (for which you need to pay a subscription) is offered for a limited time in their free dictionary - probably as a means of attracting purchasers of the full dictionary. It has nothing to do with validity of the word in question. You will note, however, that the entry for "demonstratable" is in fact the word "demonstrable", rather than an actual definition, albeit with a usage example of the former:

: demonstrable (easily demonstratable aural and visual proof — R.D.Darrell)

This says that "demonstratable" is a variant of "demonstrable" that has been recorded in use, but that "demonstrable" is the generally accepted form.

Whether or not you want to use the variant "demonstratable" is your own choice, and depends on your intended audience. Use of "demonstratable" may well annoy pedants, who will likely be turned off your work. If you happen to love the word "demonstratable", you may want to use it in order to popularise its use in the hope that it may one day become a widely accepted, and acceptable, word. If you simply want to communicate clearly and concisely, without distracting people's attention to whether or not you have used a word correctly, then use "demonstrable".