Meltdown & Spectre - Does patching the guest kernel of an unpatched hypervisor prevent cross-VM memory leaks?

From what I understand of the vulnerabilities, no - the speculative caching attacks bypass all of the CPU's protections against a process grabbing memory from whatever arbitrary address.

I believe this would include the neighbor VMs (even those patched to protect against the attack themselves) as well as the hypervisor's kernel memory space - but even if there is something that I'm missing that would protect against direct memory disclosure, there's also potential that the attacker could use their access to kernel memory to gain more complete access to the hypervisor.

You definitely don't want to risk running a sensitive workload on an unpatched hypervisor of any kind if you don't trust all of the VMs running on it.