I'm doing some troubleshooting and that doesn't appear to be the case. I found an old forum post from 2013 that states:
The Template would add the Host to the Host Group, but those hosts don't inherit settings from the Host Template, it would need to be applied direct to the host. Is it not possible then to apply a Host Template to a whole Host Group?The issue comes from the logic of applying a hostgroup to a template, then applying the hosts to the hostgroup and expecting it to inherit.
What is actually happening, the template is told to apply the defined hostgroup to everything that uses the template, not for the hostgroup to inherit checks and settings from the templates. So instead you need to apply the settings such as host groups and other templates the a template, then apply this template directly to the host or service and all groups and other settings will trickle down. Does that make sense, I understand its a tricky topic.