As of October 2019So far, not yet.
The Brave Dev team said it's on the roadmap, there are several overlapping issues (with sync, bookmarks, general browser data, and specific password import/sync) but there has been no feedback from the Devs on an implementation timeline. Very frustrating. Brave is a great browser and has lots of potential, but if it's to compete with the other browsers it has to include basic features that users expect. Password sync, or at least import and export on mobile/laptop/desktop, is one of them. Payment, Address and other browser data would actually make it comparable to other browsers...