Yes, it's possible. There's an option to enable "catalog mode" in K2's category settings. Like this:
demo.getk2.org/catalog
The only difference in that URL is that all categories, even the top-level ones, have items in them, so we basically show the sub-categories and then right below that any items directly belonging to the currently displayed category. If your items belong to categories at the very end of the category tree, then you'll navigate from category to sub-categories until you end up in the deeper category where items actually exist.
You should also create one master category for your catalog and have all its subcategories inherit the master category's settings (so you don't set the settings for every child category).
