I need a basic rule of thumb for some number (say 60 or a 100 NM) that the earth drops away from an 'absolute' straight line.....
The question seems to be answered above. But remember that the aircraft itself will be dropping away from an absolute straight line as it travels around the earth. Yes, this is negligible when compared to the earth's radius, but is not negligible at all when compared to a small change in altitude. A calculation error of 3000 feet is not negligible when it comes to flying around or through storm cloud tops!
Therefore, if you want to know if you will fly above or through a cloud seen some distance away, you must take earth curvature into account.
This is difficult without a diagram. Draw a section of the earth, with radius r and angle subtended at the earth's core of 1°. Distance across the earth's surface will be 60nm of course. Put the aircraft above the earth's surface at one radial line, and draw a tangential line (your "absolute straight line") out from it. Draw a cloud above the surface at the other radial line at the same height above the surface as the aircraft model.
The cloud is well below the tangent line - but the aircraft will still fly through it. Draw a straight line from the aircraft to the cloud. This makes an isosceles triangle with the two earth radial lines, and the angle between the tangent line and the aircraft-cloud line is half the angle subtended at the earth's centre - 0.5° in this case.
To answer your question: The earth's curvature does matter. For each 60nm you are from cloud, the cloud must be at least half a degree below your horizontal in order for you to fly above it.
My apologies if I've taught you to suck eggs here - I think this answers the spirit of your question, even if it has not given you the magic number you were after.
regards,
O8