Nope. Android Auto is simply not available on GrapheneOS
Discussion
Surely if you install all google play services and google play store it'll run then?
Nope. It's blocked at another level - Android Auto requires superuser permissions that GrapheneOS is configured to simply not grant, IIRC. I've heard of people that have compiled their own version of GrapheneOS including AA, but its not available off-the-shelf in any way.
Android Auto aren't currently supported since they require privileged OS integration that we can't easily work around.
It would be easy enough to add the privileged permissions and have it working but that goes against the whole approach. We avoid giving any special access to Google Play at all. It can only do what a regular app can do, and a regular app cannot do what Android Auto does.
Android Auto is therefore inherently not compatible with the sandboxed Google Play approach since it requires a substantial amount of privileged access to function. It would need a significant compatibility layer and additional permission systems.