Sounds like a PITA patient and one I wouldn't want to dedicate too much time to. By forgoing the anesthetic, not only do you make the patient uncomfortable, you make yourself uncomfortable treating the patient too. I've given in to the wishes of several patients in the past who dreaded the needle only to find myself sweating bullets while trying to keep from hurting the patient. You will work much faster knowing the patient is properly anesthetized.
To answer your question, topical works exactly as it's named, topically. It usually works (doesn't) on the oral mucosa past 0.5mm from the surface. Trying to get topical to diffuse through hard tissue like dentin would be impractical. I don't think it'd affect the bonding of the restorative material like some other chemicals would.
In the end, I'd focus my time more on patient management and trying to allay their fears. If they refuse to continue with the procedure with anesthetic, then maybe they're not quite right for your practice.