Hi,
About the Split-Brain question. I understand you have a stack made of 2 switches.
In a stack, only Master-Capable switches can become Master. This is configurable, and using easy-setup the default is to have 2 Master-Capable (Master & Backup). Which, in a stack made of 2, means that every switch is Master-Capable.
In such a situation, when a split-brain situation occurs, both switch will act as the Master. You have, then, twice the same config, with same IP, and that can be a problem for your network. If, for some reason, the second switch is not Master-Capable, it will reboot and act as a standalone switch.
Regarding the LAG question, are you using LACP or not? Without it, the LAG would still work imho, as only a link Up is enough. That would be bad. That's why LACP is far better to use. With LACP, the Control Plane can detect something is wrong and prevent the LAG to come Up. This is what happened, so I assume you have LACP. In that case, no traffic flow through the ports.
Please read the procedure when you rebuild the stack, to be sure of what can be the impact.