Add in the interaction between the earth and moon and really mess with your figures.
I believe the moon/earth/tide action is slowing the earth down and sending the moon further away.
Wikipedia
Structural integrity
A number of concerns have arisen about the possibly inadequate structural stability of the dam itself. Several days after the first filling of the reservoir, around 80 visible cracks were observed in the dam’s structure.[91][92] The cracks were described to be “hairline” despite their size and depth.[93] The submerged spillway gates of the dam pose a risk of cavitation,[94] which is similar to the cavitation that destroyed the spillways of the Glen Canyon Dam in the floods of 1983.
The Three Gorges Dam Project Corporation responded to the criticism of the dam integrity, saying that the project quality is under control over its 17 years of construction. Around 163,000 concrete units of the dam all passed the quality test. After filling of the reservoir, the dam deformation was within the design limit. The right side of the dam is free of cracks, which is a significant achievement of the project. An experts group gave the project overall a good rating in terms of quality
In fact, yes.
The tidal action has two effects:
Slows down the rotation of the Earth (longer days)
Speeds up the revolution of the moon around the Earth. I’m not sure if that means shorter months, though, because as the moon speeds up a bit it goes into a higher orbit.
Eventually, it will probably escape.
http://www.astronomy.ohio-state.edu/~pogge/Ast161/Unit4/tides.html - (see Tidal Braking)
So in some billions of years (about the time the Sun is slated to go nova), the Moon will be about half again as far away from us as it is now (no more total Solar eclipses!), the Earth's rotation will be exactly the same as the Moon's orbital period (around 47 of our current days by then). You'll be in daylight for around 23 days, then in darkness for about 23 more, and the Moon will appear to hang over one spot on the Earth all the time.
So damn dam may hasten that moment by...what...a few years?...big deal.
“I believe the moon/earth/tide action is slowing the earth down and sending the moon further away.”
That’s correct. The Moon moves away from the Earth about 2 inches annually.