The largest increases in spontaneous decay rates of quantum emitters can be achieved using plasmonic structures that are characterized by closely spaced metallic elements. These systems can give rise to the smallest optical cavities attainable, offering a viable solution to achieve single molecule light-matter strong-coupling. On the other hand, their optical response might be strongly affected by nonlocal and quantum effects of the metal electron gas. In this work, we analyze the impact of nonlocal effects on the emission properties of a single quantum emitter coupled to a plasmonic system characterized by deeply subwavelength gap regions, in both the weak and the strong-coupling regimes. We find that the presence of nonlocality imposes strict limits to the achievability of strong-coupling with single molecules in apparent contrast to recent experiments, suggesting that a more refined theory might be required …