I suppose technically it is -- after all, the reason the Sun is due to burn out in 5 billion years or so is because it's burning through its energy, and that energy is being dumped into space, and if we suck that energy up faster and more efficiently in our patch... I may try and check this some time, not sure it's really the same thing.
More seriously, though: the Moon is receding from Earth gradually, due to energy loss from e.g. tides, and if we did extract yet more energy from the tides then the Moon would recede faster, but off the top of my head I doubt it would make any significant difference unless we were using tidal power whenever and wherever it was possible to do so, across the whole world. Even then I don't think the energy thus extracted would be (any more than) comparable to that already lost due to friction with the seabed.
Tidal power is, or ought to be, part of the answer to our energy needs, but not all of the answer. The potential environmental damage is one reason, though we've done enough to devastate large parts of the ocean and the Earth already. Also, it's not a good idea in practice to rely solely on a single form of energy, especially one such as tidal, because of the risk of something going wrong (either by accident or as a deliberate attack) -- with only that as a source of energy, such an accident could be a major disaster. Let alone the cost to set the thing up in the first place, or to maintain it. Meanwhile most renewable sources of energy find it difficult to cope with changes and surges in demand such as the "half-time in a football match" or "just before the next episode of Corrie" surge, when everyone watching goes and puts the kettle on. For such surges you need either to develop a way of efficiently storing energy that can also be called upon quickly, or an energy source that can be controlled as needed. At the moment only certain HEP stations and conventional fossil fuel power stations (and, to some extent, nuclear power stations, see below) can cope with these rapid surges, but the technology is expanding into diverse renewable sources also.
The key word, though, is diverse. Relying on just a single source of energy, however attractive, is not the answer.
A few sources:
http://www.darvill.clara.net/altenerg/pumped.htm
http://www.nationalgrid.com/NR/rdonlyres/49736B61-06E4-4241-AF0B-8E7D84053AF7/1227/Nick_Easton_A_day_In_The_Life_Of_.pdf
http://www.claverton-energy.com/nuclear-power-is-flexible-in-its-output.html
http://www.kombikraftwerk.de/index.php?id=27