No for Whispersync. Kobo only offers synchronization for books purchased through them. On the other hand, KOReader does offer synchronization.
Self hosted in Docker, I browse to the book I want, add it to a ‘shelf’ that is synchronised. then on the Kobo I press sync. It downloads.
I used a guide that was something like this:
https://jccpalmer.com/posts/setting-up-kobo-sync-with-calibr...