I just created a test case, and [show_posts] on a default type page template does show sticky posts at the top when the show sticky posts option is checked.
If you are using [show_posts] on a post instead of a page, there could be issues at the short code is not really designed for nested display.
I would also think you could us a Page with Posts for the same purpose as that will show posts by title only.
For example, see this page showing list of posts with the first post being a sticky post:
http://guide.weavertheme.com/contents
Whatever content you put in the content of a Page with Posts will show above the posts shown.