No. WeaveGrid will not automatically charge your battery ahead of a Grid Event.
However, this does not stop your home energy system from doing so, depending on how you’ve configured it to operate.
Details for Enphase battery systems:
By default, your battery settings will be configured to help maximize your performance reward earnings and comply with program requirements. To help maximize your performance rewards, your battery will be set to Full Backup mode six hours before each event start. Your battery mode will revert to the original settings once each event is complete. These changes will occur automatically before and after each event.