Yes, you can unplug and re-plug your device to Control Center. However please note the process for disconnecting and re-connecting devices to Control Center.
When you connect a device to Control Center, you configure the HDMI port for that specific device. When you remove a device from Control Center, you will be prompted to 'Remember' or 'Forget' that device. Choose 'Remember' if you plan on reconnecting the device back to the same port on Control Center. If you choose to 'Forget' the device, you will need to setup the device again if/when it is reconnected.
If you choose 'Remember' but decide to either use a different port or not reconnect the device, go to Settings> Devices> [device name]> Cable Detect and select the "Enable" option, then confirm the selection.