You can still achieve determinism by treating the measured delta-time as an input, and resimulating the game with recorded delta-time. This may not be feasible on public servers, but is definitely feasible for professional play where determinism is important to rewind games due to bugs which affect competitive integrity.
In StarCraft II you can resume from replay (and maybe in previous games as well), but I don't know if this has ever actually been used due to bugs in the game engine during competitive play.
I implemented a debug replay system for an American Football game when I worked at Sony. The AI hierarchy and all animation and physics state was recorded and game could be rewound to figure out why an NPC made a poor decision. Only needed to track state for the duration of a single play. This was on PS2 which I think had 32MB of memory but the dev systems had an extra 96MB which we could use for this sort of thing.
Yeah you _could_ but I fail to see why you would ever do this. It's also not feasible to synchronize the client with the server in real time with this input.
You don't need to synchronize the server and the client. The point of determinism is to be able to reproduce game states deterministically, not to have people play the video game deterministically. Again, this is to "undo" bugs in pro play (Chronobreak).