Not quite, but as the paper says:

    Corollary:  No  probabilistic  regular  grammar
    exhibits criticality.

    In the next section, we will show that this statement is
    not true for context-free grammars (CFGs).

That is, there exists CFGs that exhibit criticality. Programming languages are often parsed by CFGs, so it's likely that some programming languages exhibit the same criticality structure as natural languages.