Can an
average GA plane take off with a load great enough to cause damage in
the event of hitting some chop? I don't know, but I suspect that should
be the least of one's worries.

That depends on the airplane. If you're dealing with a normal category
airplane with old and possibly deteriorated wing structure, I sure
would worry about it. Some of the heavier Cessna twins that served a
lifetime in hauling cargo (where, contrary to regulations, gross weight
is often exceeded, as is zero fuel weight on short runs). Consider
these accidents:

http://www.ntsb.gov/ntsb/brief2.asp?...FA123& akey=1

This is a narrative of the NTSB accident investigation that prompted
the original Airworthiness Directive against the 400-series Cessnas.
Note that the blame is placed on a manufacturing defect, but that does
not diminish the role that repetitive misloading may have played in the
failure.

http://www.ntsb.gov/ntsb/brief2.asp?...FA208& akey=1

This is narrative of an NTSB accident investigation of a Cessna 402
engaged in Part 135 cargo operations that crashed into the Caribbean
Sea. Only parts of the aircraft and some cargo were recovered, and no
probable cause is listed. However, known circumstances outlined in
this report point to wing spar failure, the report suggests that
misloading played a factor.

Is this is a factor overloading a C-172? Not just no, but hell no.
But here's the problem - you get away with it on a C-172, and unless
you understand what you did and why you did it, you have no frame of
reference to know you can't do the same thing on a C-402.

CG seems a more pernicious issue to me, as the plane's behavior can
fool you. Chances are you won't realize you're thoroughly screwed until
after you're up in the air without any good options.

Well, that's overstating the case by quite a lot. The cg needs to be
quite a bit aft of limits before normal flight and a normal landing are
a problem. Oh, you'll feel the reduced longitudinal stability, but it
likely won't be bad enough to keep you from landing the plane. Just
don't stall. Also realize that as weight increases, generally the cg
limits narrow.

The real issue occurs in a tailwheel airplane. A tailwheel airplane
loaded aft of cg can be a real bear on the ground - lots of weight aft
of the mains give it very poor lateral stability.

In addition to
takeoff CG, I'd also compute CG with half fuel and very little fuel,
just in case.

It's not a just in case. In the Beech Bonanza, it's a real issue. As
you burn fuel, cg moves aft - and unless you have some real big boys up
front and little or nothing in back, you're never far from the aft
limit anyway. On the other hand, you have to try real hard to get a
Brand C or Brand P aft of limits.

Michael