Okay, I've already accepted the answer from the fellow who answered me when I asked the question. But I want to add my own answer here, too, to report my experience.
No, you don't have to stop Sharepoint.
I took a Windows Server (2008) backup with Sharepoint running using the "full" "bare metal" option. I put the backup on a network folder. Then I hooked up an old Optiplex I had lying around and booted it with the Windows Server 2008 installation CD. I used the options for restoring the full backup. Everything went very well.
Active Directory was all there (I made sure this machine was not online when I booted it after the restore!), DNS was there, Sharepoint was there - I could navigate all the pages just fine. Of course, the drivers were mismatched, and my Optiplex didn't have the same resources as the PowerEdge R610, but it was all there and it all worked, at least in my cursory check. I noted that the most recently created pages were also present - anything that was made before the backup began was all there.
So, in conclusion, yes you can make a Windows Server Backup whilst Sharepoint is running, and I've done it.