I do have an Onyx Boox tablet, the Note 2 plus to be specific, and I do run Calibre and calibre-web on my home server.
Though I don’t actually use calibre-web at all, and the full flat calibre only to organise the collection. Usually I just copy the files to my tablet manually, but I do leverage the built-in RSS reader in Calibre to create my own epub “newspaper” periodically, which is synced to the tablet by Synching.
I have also used to have (actually still have it, but not use it) an old Kobo touch with Koreader, and I intended to download the books wirelessly using the calibre-web, but honestly, I just copied it over an USB anyway…
If I think about it, I could simply sync my whole library over Synching.