Yes, when there is not voltage on VBUS,FX3 will use VBAT supply for power
When VBUS is power cycled, the FX3 device has the ability to detect the presence of VBUS (this can be controlled using CyU3PUsbControlVBusDetect API). So, this will help to identify whether the device is connected to the PC. Although, with the VBUS goes of, the FX3 device will be active by self-power VBAT. Once it detects a VBUS, then it can send the descriptor to the host to enumerate again.