I think you underestimate the state of the art. Considering how often modern systems use random numbers I can't imagine this case not being handled, by disabling any hardware mechanism that could introduce non-determinism at the very least.
Looking at the VMware FT docs the hypervisor for the primary VM very thoroughly records anything that could change state and does not pass it through to the primary until it is transmitted and receipt acknowledged by the hypervisor for the secondary VM. Features such as SMP or hardware MMU are disabled as their state can't be recorded and could introduce non-determinism. Each event is injected into the secondary at the same execution point. That certainly has to work with nanosecond timing, from the point view from inside the secondary VM. According to wall clock time the secondary will always be lagging behind, the demos show lag in the millisecond range, but because events are recorded it can be brought up to current during a failover event, so no state should be lost.
If you are interested you may want to do a little research on the topic, on your own. When I get this set up in my test environment I'll definitely run though creating ssh keys and whatnot to validate my understanding that this does work.