In short, No. Shredded paper clogs sorting machine, especially during the paper quality sorting process. In addition, many contaminants tend to hide in shredded paper, such as plastic. By shredding paper you are also shortening the length of piper fivers and therefore making it less valuable and shortening its recyclable life.
From Eco Cylce - Here are some tips for minimizing your "shred" impact:
1. Spare the shred. Please avoid shredding paper whenever possible. Shredding shortens the paper fibers and therefore cuts the recycled life of paper in half.
2. Shred paper only, no plastic. Be careful not to include items like faux credit cards made of plastic, promotional stickers or sheets of address label stickers.
3. Rip it, don’t shred it. Instead of shredding, consider ripping off sensitive elements of your documents (bank account numbers, social security numbers, etc.) and shredding or ripping only those parts, leaving the rest of the page whole and recycling it with your single-stream recycling.
4. Mark it, don’t shred it. Another alternative to shredding is to simply black out sensitive information with a permanent black marker, taking care to mark both sides of the paper if the content is still visible from the back. You can then recycle the paper whole in your single-stream bin.