</font><font color="blue" class="small">( Gravity distorts the laser...)</font>
By older models of physics, this was one portrayal of reality. The most modern models, however, portray a different reality. According to such models, gravity, rather than accelerating mass and energy, warps the space through which matter and energy waves move. Accelerometers on the Hubble telescope indicate that it is moving in a straight line (the accelerometers do not sense the "centrifugal force"-to borrow a term from Newtonian models) of Earth's gravity. Earth's gravity warps the space through which the satellite travels and as it moves though that space the accelerometers sense no delta V in any direction, yet the telescope moves in an eliptical orbit relative to the earth.
The same gravity, said above to affect the laser, also affects the space within which the structure exists and the light that provides the so called "line of sight". Light from the laser and light which provides the line of sight both travel through the same warped space. If one were to assert that gravity bends the laser beam but not the sunlight enabled "line of sight" to which the laser is being compared and contrasted, such an assertion would be fallacious.
The width of the moon, as measured in degrees and minutes from the surface of the earth, is actually slightly wider than that of the sun as measured from the surface of the earth. During a total solar eclipse, however, a "corona" is visible around the moon. This effect is not from Luna's (the actual name of Earth's moon) gravity bending the light from Sol (the actual name of Earth's star). Instead, Luna's gravity warps the space through which the sunlight is traveling, causing the appearance of the corona.
If you build a highway around the equator and every portion of it were at the same elevation MSL, then set in motion a car whose apparent speed never changed, an onboard accelerometer would indicate the same thing that an orbiting satellite would (discounting minute differences in Earth's density and shape which do cause minute gravitational differences at the surface): no delta V, even though the bed of the roadway is curving. Now since the surface of earth itself curves at a tighter radius than its gravity warps the space around the earth, the mild "curvature" of the space through which the beam travels, will not match the curvature of the earth's surface. You are correct regarding necessary compensation on projects like the English Channel Tunnel.
As you also say, a laser becomes more out of level in direct proportion to its distance from the source. This is because the light waves are relatively close to being parallel, but are not perfectly parallel. Thus, over a distance, the beam diffuses as does any flashlight, but over a greater distance.
Lastly, for those who may not be aware, the word LASER is an acronym for Light Amplification by the Stimulated Emission of Radiation. "Lazer" is an intentional misspelling for the purpose of a copyrighted brand name.
