Yes if you define a moon as any sub-stellar body orbiting a more massive sub-stellar body. On SpaceEngine I've encountered several moons that have a higher surface gravity than their planets. A common definition of a moon is what I've stated above. If a more massive body is much less dense than the moon, and thus much bigger while the moon is less massive but even much smaller and thus much denser, it has a higher surface gravity. But since it still has the smaller mass and thus gravity at the same distance, it counts as the natural satellite.
Titan and Ganymede are bigger than Mercury, but less massive and dense, therefore they have a lower surface gravity than Mercury (Titan 0.138 g, Ganymede 0.146 g and Mercury 0.377 g). Pluto is bigger than Eris but Eris is more massive, therefore Eris with 0.084 g has a higher surface gravity than Pluto with 0.063 g. In the mentioned cases if the masses of certain bodies were larger, some of them would probably count as planets while still having a lower surface gravity than their moons if they orbited each other. Actually, Io with 0.183 g has a higher surface gravity than Ganymede with 0.146 g despite Ganymede being more massive.
However there's no official definition of a moon and the current understanding is somewhat unscientific (not to mention the definition of a planet). If the two Martian satellites orbited directly the Sun they'd count as asteroids. If Titan and Ganymede orbited the Sun directly they'd count as (dwarf) planets. However because all of them orbit planets everything that orbits a planet falls into the same category of a moon with no official distinction among them. One should judge a body by what it is, and not its orbital parameters. In this case, if we set a distinction based on mass, it still would be possible that a moon has a higher surface gravity than the planet it orbits for the same reason mentioned in the first paragraph.
If you consider any bodies where the barycenter is between them a double/triple/... system then I doubt that it's possible for a moon that has its barycenter within the planet to have a higher surface gravity than it. The planet would have to be so large that it would hardly be possible. In such a case I'd say no. However, if you consider Pluto-Charon a double (dwarf) planet system you'd also have to consider Sun-Jupiter a (half-star/half-planet) binary sytem (and call it Solar-Jovian System) and Earth-Moon would also have evolved into a binary system in billions of years so that the Moon would become a planet despite haven't changed in itself. That's why it's good that Pluto-Charon were not classified as double planets and/or why a body should be judged solely by what it is.