That's about it. I want to make some vinegar pickles (from the Momofuku cookbook, if it matters). My partner is on a diet that forbids refined sugar but allows honey. Will honey work for this purpose?
Sugar is not critical to the pickling process - it exists primarily as a flavorant.
Pickling preservation requires one of two methods - either immersion in vinegar of a sufficiently low pH to kill off unwanted bacteria, or through natural fermentation with probiotic strains of bacteria.
Honey is known to have antiseptic and antimicrobial properties. When using natural fermentation, one might think that there may be a risk that the added honey will kill off probiotic bacteria before they establish a stable population, allowing other unsavory bacteria to grow. However, most brine-based recipes already include known antimicrobial herbs such as mustard seeds, garlic, cinnamon, or cloves. Honey shouldn't be any different than the addition of these spices.
When using vinegar to pickle, there is no reason to be concerned about adding honey.
Regardless, it is important to note that honey will have a distinctly different flavor profile from pure sugar. Perhaps try it in a small batch before committing to "large scale" production.