The way I see it there are a couple of ways this can shake out:
1. If you have a sync server that only relays the updates between peers, then you can of course have it work asynchronously — just store the encrypted updates and send them when a peer comes back online. The problem is that there's no way for the server to compress any of the updates; if a peer is offline for an extended period of time, they might need to download a ton of data.
2. If your sync server can merge updates, it can send compressed updates to each peer when it comes online. The downside, of course, is that the server can see everything.
Ink & Switch's Keyhive (which I link to at the end) proposes a method for each peer to independently agree on how updates should be compressed [1] which attempts to solve the problems with #1.
[1] https://github.com/inkandswitch/keyhive/blob/main/design/sed...