Google assistant local fulfillment with SSL

I have HA on a public IP, with an SSL cert.
The public IP is also local (yes I have routable addresses in my home, there is no NAT in my house). (my real domain redacted, and replaced with my.local.domain.com)

Home assistant is on https://homeassistant.my.local.domain.com:8123
Can I use Google assistant with local fulfillment with minor changes to the config?

Example:
Instead of using _home-assistant._tcp.localcould I use _home-assistant._tcp.my.local.domain.com which has an SSL cert on it?

And instead of .*\._home-assistant\._tcp\.local can I use .*\._home-assistant\._tcp\.my\.local\.domain\.com which has the ssl on it.

I’m using Google Assistant manual setup with Google Cloud platform config