You'll be able to lay your Xbox Series X down flat but the attached stand might mess with your aesthetic.
Microsoft has pushed the upright, chonky obelisk orientation of Xbox Series X in all of its marketing materials, however it has previously confirmed that the console will work on its side as well. Sounds like the best of both worlds, but when Microsoft sent out dummy units for demonstration purposes, one caveat to that idealized form quickly became apparent: there's a little circular stand on the "bottom" of the console, and it is not removable.
IGN executive editor Ryan McCaffrey confirmed with Microsoft that the plastic stand is permanently attached to the bottom of the console. I guess you probably could remove it with some effort, but it might mess up the grill on the bottom of the console and it would definitely void your warranty.
One of the most common questions I've gotten is if the round stand on the bottom of the Series X is removable, in the event you choose to lay it on its side. I couldn't find a way to take it off, and I just confirmed with Microsoft that it is indeed not removable. So just FYI!September 10, 2020
For what it's worth, the power button's Xbox logo is also oriented to be upright when the console is standing vertically. So Microsoft is definitely sending some signals that this thing would really look best if you were to just keep it vertical, please.
If staying horizontal and looking good are essential to your gaming setup, you could give the Xbox Series S a look instead. The light-up logo is even designed to be right-side-up when the console is laying sideways. Our Xbox Series X vs Xbox Series S guide will help fill you in on the finer details of the differences between the two consoles.
Speaking of which, some developers are worried that the lower specs of Xbox Series S may hold back the potential of the next generation of games.