An excellent question. I tried to do so some 6 months ago and never got the notification of/link to download the files, and have since been using other tools to backup cached copies of my bookmarks.
I love Pinboard and intend to keep using it while it's still usable, but I do have serious concerns about its long-term sustainability and am continuing to look at other options. Raindrop.io isn't bad from a saving content standpoint, and I understand Evernote is similar, but they aren't nearly as good (imo) at using an organized tag system to manage a large and growing library of bookmarks.