In general, this is the basis of organic chemistry’s notion of functional groups: a reaction will occur if a given functional group (here: benzylic hydrogen that can be turned into a benzyl radical easily) is present regardless of any other groups in the molecule. Thus, in theory, the reaction should occur just as well.
In practice, functional groups are never fully innocent. They can either disturb the entire reaction by interfering with the mechanistic pathway (e.g. you cannot perform Paterson aldol reactions in the presence of alcohols) or they can subtly affect the electronic and steric parameters of a molecule to ease or inhibit a reaction. For this reason, journal articles that establish novel transformations often ‘synthesise a table’ — i.e. they take multiple related compounds and perform the reaction for each to show whether it works with a given functional group at all and how the yield is affected.
In this case, the benzylic radical intermediate is an electron-deficient species. Fluorine is an electronegative substituent that destabilises electron-deficient species. However, fluorine is unlikely to interfere with the generation of radicals or react with them. So without having consulted the literature I would predict the reaction to work but require longer reaction times, higher temperatures or give lower yields.