It seems to be fairly random, but I've certainly seen them use plastic bags for shipping. These are the two most common styles, with one being a bag, and the other being a bubble-wrap envelope.
I can't see it being cheaper, since those packages aren't free. Faster? Not sure about that, either. Amazon automates a lot of their process, and the separate items would still need to gather in one place to be shipped together anyway. Packing a half dozen separate items is surely less efficient than packing everything in one box.
Again, this wasn't a problem a few years ago, when everything would come in a single box. The greenwashing by Amazon about their plastic bags is 10 steps backwards, IMO.