Actually, I have an artist friend who regularly gets her pastels dry mounted after they are done. I have to say I never had the nerve to try it myself. Best to do a trial first.
Foam core comes in an acid free version.
I think the larger problem will be how to avoid damaging the drawings. Anything that touches the charcoal will smudge it, and plastic will produce static, which will lift the charcoal off the surface, and deposit it onto the plastic. If the pencil work is soft, it will likewise fall victim.
If you want to just show samples, can you make a high quality print of the drawings from your computer?
If your intent is to use the drawings to get commissions, I really think they need to be properly matted, framed, and shown in their best light.
