Could the High Sierra root bug have been exploited over SSH?
The login mechanism for SSH and for Aqua are two entirely different things.

sshd is the OpenSSH daemon (what allows you to log in via SSH) is sourced from BSD.  This vulnerability doesn't exist there.  

Additionally, the default configuration for OpenSSH is to disalow the root user to login whereas this bug/flaw allows you to log in as root with no password by simply pressing a button twice.