Does the MX still function in the event that the appliance is unable to communicate with the cloud?

Yes, the appliance will continue to operate on the last known good configuration and enforce all configured security policies. While disconnected from the Cisco Meraki cloud, configuration changes are limited to basic uplink and port settings accessible on the local status page until such time as the appliance reconnects to the cloud. Analytics and reporting data will also still be gathered while disconnected and will be available when connectivity is regained.