I have the same library for both kodi and Jellyfin, but for now it’s jellyfin that I download offline media from. On a good connection it usually takes about 3-5 minutes for a yatse library sync to complete, and it seems to be about the same for both backends.
Sometimes during sync the TV shows library in the app disappears (shows “no media”, or just show a few of the series in the tv-shows category), but it comes back when the sync is complete. When on a good connection this can be a mild annoyance to not be able to watch anything for a few minutes. What’s worse is that during this time I can’t start any of the offline media files I’ve previously downloaded (as the library looks empty). The files are still there; they do not need to be re-downloaded after sync, but they cannot be accessed.
The big problem is when yatse decides to do a sync when I have a bad coverage or otherwise unreliable connection. This can make my offline files unavailable until the connection improves and the sync completes. For me this can occasionally be hours away.
I suppose disabling automatic sync would “solve” this particular problem at the cost of everyday convenience, but I really would like the the library to be fully available during syncs, or at the very least be able to access already downloaded media.