No I think that kind of collection is collection of books not collection of stories, and I think this award is for collection of stories. They usually focus on giving out awards for individual books, even books in a series.

So you can give an award to book 3 in a series if it's a particularly good book (you'll see George Martin was nominated for a Hugo for book 5 in his series, and Jim Butcher for book 15, Harry Potter, Ender, actually a lot of those Hugo noms are in a series). It's harder to award an entire collection of books, though I know the Hugos have a mechanism for doing so as long as the series is complete and none of the books has won before (in 2014 for Hugos you can see "The Wheel of Time" series).