We have applied some DNS configuration to both cluster members (identical). The second one works without issues. I would expect to have some delays if DNS fails to resolve something but not a full inability to interact with the devices.
HTTPS access to the Gaia portal works on VSX, just with very few options like updating the Deployment Agent and installing/uninstalling hotfixes. On the second node that page is accessible without issues.
The provisioning process went like this:
1. We received the appliances;
2. Used LOM to apply initial configuration (IP addresses on the interfaces, routing);
3. Used HTTPS to complete the setup on the Gaia Portal;
4. Enabled HA + VSLS via cpconfig;
5. Created a VSX cluster on the Smart Console;
6. Installed initial policies on VS0 on both members;
7. Created virtual switch and virtual firewalls + policies for the latter;
8. Installed the virtual firewall policies.
All steps above completed without issues and for several days the problematic node was accessible.