Aside from the risk of choking (which is obvious), is it dangerous for
a human being (child or adult) to ingest cotton?  I'm talking in
quantities similar
to seven or eight standard "cotton balls" at a time, possibly over a
number of days.  Could this clog or injure the intestines, or would
the body most likely eliminate it without problems?

I think it would be a source of fibre. Supposedly, it is caused by a
lack of nutrients.