Yes, it’s easy. You upload the .doc or .pdf file using your media uploader, just as if it were a picture. Then you copy the link to the file you’ve just uploaded, highlight some text in your post, like
“Click here to download this file”
hit the link icon, and when the box pops up asking for the URL, you put in the URL of the file. It sounds more complicated than it is.
You can anchor it on text (as above) or add a picture and add the link to the picture. Just remember; the picture has to be uploaded separately, because .doc and .pdf files won’t show as images on a WP.com blog.