Solarmass They were before Solus moved to a newer version of Nautilus and Josh found a way to nativelly implement desktop icons in Budgie. And by implement I mean they technically exist and you can have then arranged alphabetically on your desktop starting with the upper left corner and star programs by clicking or duble clicking them (man, what functionality!)
But rearranging them? I mean, if you think that going into Nautilus, opening the desktop folder and renaming the files there counts as rearrangement, then sure. You can "easily" rearrange the desktop icons.