The literal answer to your question is no, Safari can't do that (I don't know of any other browser that can do that either).
There are two SIMILAR solutions but they are not LITERALLY what you're asking for.
The first is to edit Top Sites to "anchor" your preferred sites (this is what I've done -- in effect, 24 home pages!). Set your default to open Top Sites, pick the site you'd like to go to today from the list of 24, and done.
The other is to put your preferred list of sites into a bookmarks folder, and put the folder in your Bookmarks Bar. The folder can hold as many sites as you like, but I recommend a dozen or less (you'll see why in a moment).
Set Safari to default open to a blank page. Click on the folder in the Bookmarks Bar. Go to the last item, which is always "Open in Tabs." All the sites in that folder will now open in tabs. You can read the first (or 10th for that matter), close it when you're done, it moves on to the next site and so forth. I do this with my short list of quality news sites, and read them in the morning over breakfast. Fascinating to see how different sites will cover the same stories, or the different stories they choose to emphasise.
Hope that helps you.