After you put your device in developer mode, it is essentially a Linux box, like any other. Depending on how heavy your "standard Linux binary" is, it will most likely work; the problems you’ll have will be that the “X library is not installed by default,” which you can get from any other distribution, and not “ChromeOS is so strange that nothing will happen.”
You won’t be creating software on the Chromebook itself unless you install GCC and its associated binding — you need to set up your development environment on a separate machine; see http://www.chromium.org/chromium-os . You should probably be advised that this is not trivial, and it is recommended that you use a “clean pipe and development machine”.
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