Answer:
It doesn't depend on the grape variety, it depends on who makes it!
There could be wineries that have chosen organic methods to cultivate their vineyards, as well as there could be wineries that use traditional methods.
If you want to drink Aglianico wine from organic grapes, look for this symbol (http://www.ccomemagazine.it/wp-content/uploads/2009/09/biologico.jpg) on the
back label.
(According to the law, "natural wine" doesn't exists; a natural wine is what you get from grapes cultivated with organic methods).
Cheers,
Giovanni