It depends how close the binary stars come within each other... as you say, your planet is close to its star, like Mercury. To have tidal effects from the other star, it would have to come so close it may even disrupt the orbit of the planet's parent star, and unpredictable things would happen. It may be more likely the planet would be flung out of its system rather than have a steady tidal friction that you want.
In my planetary science studies, I've found that the best way to ensure steady active tectonics is to have a rocky planet, about earth size or larger to ensure a hot core, and with a metallic core to ensure magnetic fields.
Info about binary stars and their planets:
Alpha Centauri A has 1.1 times the mass and 1.519 times the luminosity of the Sun, while Alpha Centauri B is smaller and cooler, at 0.907 times the Sun's mass and 0.445 times its luminosity. The pair orbit around a common centre with an orbital period of 79.91 years. Their elliptical orbit is eccentric, so that the distance between A and B varies from 35.6 AU (astronomical units), or about the distance between Pluto and the Sun, to 11.2 AU, or about the distance between Saturn and the Sun.
Alpha Centauri C is about 13,000 AU away from Alpha Centauri AB. [wont disrupt A or B’s planets]
From https://en.wikipedia.org/wiki/Habitability_of_binary_star_systems :
In non-circumbinary planets, if a planet's distance to its primary exceeds about one fifth of the closest approach of the other star, orbital stability is not guaranteed. Studies of Alpha Centauri, the nearest star system to the Sun, suggested that binaries need not be discounted in the search for habitable planets. Centauri A and B have an 11 au distance at closest approach (23 au mean), and both have stable habitable zones. A study of long-term orbital stability for simulated planets within the system shows that planets within approximately three au of either star may remain stable (i.e. the semi-major axis deviating by less than 5%). The habitable zone for Alpha Centauri A extends, conservatively estimated, from 1.37 to 1.76 au and that of Alpha Centauri B from 0.77 to 1.14 au—well within the stable region in both cases."