License keys are the same for 6.0/6.5/6.7 so no issue there: VMware Knowledge Base
If they are running any workloads on their environment that they care about, they are already taking a huge risk with not having a contract.
ESXi 6.0 is already out of support, even if they did have a contract.
It is best practice to run vCenter Server and ESXi on the same version if possible.
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Technicly you will not get a problem because the license keys did not change within 6.x and VCSA 6.7u3 can manage 6.0 Hosts.
Legally....it depends. If their Subscriptions ends before 6.5u3 becomes available your not "allowed" to use that version.
Question: What vSphere Edition they have in use? The small Essentials bundle costs 62,- EUR Subscription per year.
Moderator: Thread moved to the vCenter Server area.