If a sub-process gets OOMKilled and the container doesn't die, then it's most likely that the parent process didn't handle that scenario. In which case the health-check wouldn't cover that issue.
It's not clear to me what happens after the OOM. Does the init process restarts the daemon? I would argue that it shouldn't.
If the process stops responding to a healthcheck, it's the scheduler's responsibility (k8s in this case) to handle it. Crashes in this case should be handled in a similar way, whether it's due to OOM or a bug.
If a sub-process gets OOMKilled and the container doesn't die, then it's most likely that the parent process didn't handle that scenario. In which case the health-check wouldn't cover that issue.