Is it possible or has anyone explored the possibility of capturing static electricity for supplying electrical loads on an aircraft?
No, it is not.

To use electricity to do work, you need:


two thigns with stable potential difference,
large amount of charge and
good electrical connection to both terminals


And static electricity does not really give you either:


the amount of static electricity collected depends significantly on atmospheric conditions,
the total charge collected is tiny even though the potential increase can be huge and
one of the terminals is outside air and the electrical connection to it is really poor (if it wasn't, charge couldn't accumulate on the plane).