The current study investigates whether some of the variation in h-production observed among Quebec francophone (QF) learners of English could follow from their at times assimilating /h/ to /ʁ/. In earlier research, we attributed variation exclusively to QFs developing an approximate (“fuzzy” or “murky”) representation of /h/ that is not fully reliable as a base for h-perception and production. Nonetheless, two previous studies observed via event-related potentials differences in QF perceptual ability, which may follow from the quality of the vowel used in the stimuli: /ɑ/ vs. /ʌ/ (detection vs. no detection of /h/). Before the vowel /ɑ/, /h/ exhibits phonetic properties that may allow it to be assimilated to and thus underlyingly represented as /ʁ/. If /h/ is at times subject to approximate representation (e.g., before /ʌ/) and at others captured as /ʁ/ (before /ɑ/), we would expect production of /h/ to reflect this representational distinction, with greater accuracy rates in items containing /ɑ/. Two-way ANOVAs and paired Bayesian t-tests on the reading-aloud data of 27 QFs, however, reveal no difference in h-production according to vowel type. We address the consequences of our findings, discussing notably why QFs have such enduring difficulty acquiring /h/ despite the feature [spread glottis] being available in their representational repertoire. We propose the presence of a Laryngeal Input Constraint that renders representations containing only a laryngeal feature highly marked. We also consider the possibility that, rather than having overcome this constraint, some highly advanced learners are “phonological zombies”: these learners become so adept at employing approximate representations in perception and production that they are indistinguishable from speakers with bona fide phonemic representations.