No, standard transliterators like Latin-Katakana are designed to always terminate. What the article demonstrates is that the underlying rule language is powerful enough that one could write custom rules that loop infinitely.
In practice, the ICU implementation does limit the number of rewrites, even though the specification doesn't.
I've been wondering for a while if anything in Unicode could accidentally compute. It turns out that UTS #35 transliteration rules are Turing-complete. I show how to compute Collatz with just 3 rewrite rules running on stock ICU.
Indeed. The Jira rules implement test-then-decrement correctly, but the notation was ambiguous. I’ve fixed the pseudocode so that the test explicitly precedes the decrement. Thanks for the careful read!
In practice, the ICU implementation does limit the number of rewrites, even though the specification doesn't.