I'm not convinced plastic is the correct term, though it could be, plastic has many definitions, depending on context. I will have to do some research.
Its not the common term used when discussing smokeless powder though...
Normally, when I think of something as a plastic, I think of something with a petro-chemical base.
again, I'll need to do some study, its been a long time since I was involved in that branch of chemistry. Cellulose is the base material for many product, some of them could be considered "plastics", some aren't. Most paper is still made from cellulose (today, generally a wood pulp,). Though other plant fibers are also used for different kinds of paper.
Take a cotton lab coat, spill some Nitric acid on it, don't rinse it out, and after a little while, the coat will burst into flames. Rinse the nitric acid out, just enough to prevent self ignition, and you get a fiber material that will ignite easily and burn VERY fast. This is the origin of guncotton, which was developed into gunpowder for artillery and small arms, over time it became the smokeless powder we know today.