Yes and no.
There are two ways to do this:
- Make them a co-author.
- Just provide access to the manuscript.
Option 1 is easiest, but then they show up as an author, which is not true. (We don't have an editor role for only some authors yet.)
Option 2 is probably what you want, but varies based on writing mode. If you're using Dropbox, then you'd just share the Dropbox folder.
Now, they would not be able to trigger previews with Dropbox mode, however. That can only be done by an author currently, or by post-commit hooks on GitHub and Bitbucket. (So, if you were using GitHub, all you would need to do is give them push access to the repository, and then a push could trigger an auto-preview or even, based on the hooks you set up, an auto-publish.
If you want to go that route you can switch writing modes on your book, but most editors currently are not technical enough to use Git. The GitHub web user interface, however, may be doable, if they are fine with working there...