By adding a tidal power-harvesting plant you're effectively adding extra resistance to the motion of water, which leads to a tiny bit more efficient tidal braking - the slowing down of Earth's rotation and a recession of Moon's orbit. The flow of water is more obstructed, so it does a bit better job at dragging on the surface.
This is, however, a minuscule amount when compared to the braking the regular motion of water exerts due to the way the ocean beds and continents are structured, which in turn is not enough to tidally lock (i.e. deplete the potential for extracting tidal energy) the Earth to the Moon over the lifetime of the Sun.
Additionally, even in principle, full tidal lock of Earth and Moon is not possible, as at some point tidal forces from the Sun would take over, disrupting the system. That is, you can't have a situation where our planet is locked both to the Sun and the Moon, so some tidal interaction is ensured for as long as the Moon remains in the system as a freely orbiting body.
There will be a gradual reduction in efficiency of tidal power as the Moon recedes and Earth slows its rotation, though. But again, gradual enough so as not to be a practical worry for millions of years, if ever at all.
If you're still concerned about the effect of human activities on the process, I suggest the following exercise: estimate the current energy consumption of the human race, assume it's all produced by tidal power plants at typical efficiency, and compare it to the energy required to completely stop the rotation of the Earth (which is an o.k. approximation of a tidal lock).
Dave