SSL session caching

[CJ Ess]

In my current setup I have nginx behind a load balancing router (OSPF)
where each connection to the same address has about 16% chance of hitting
the same server as the last time.

In a setup like that, does SSL session caching make any difference? I was
thinking it through this morning and I'm betting that the browser would
toss the old session ID unless it happened to be routed to the same
backend, because in the other cases the backend servers would respond they
don't know the session. Is that correct?
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