Yes, if you run product+solvent and solvent alone, then you can tell if there is a difference. You might also want to add a water or buffer control as well to see the background without solvent.
Many years of antimcrobial study and application offers that "solvent control" ignores synergy - a well-known phenomenon found with low levels of solvent, esp ethanol, and antimicrobials. It's also pretty silly - generating useless irrelevant data - to force fit an insoluble antimicrobial into an assay that demands solubility when the solvent itself precludes practical application.
In OP's eagerness to get ZOI data, the phenomenon of acetic acid solubility is ignored. Is this pH dependent? If so, through what range? Presuming this is a novel compound, what does it say of the mode of action/molecular dynamics.
If this is another "natural" eye of newt/toe of frog - not worth a discussion.