Yes, you can absolutely use the espresso machine without the tablet. If you completely turn the tablet off and remove it, functions like the flush and steam will still work perfectly. You can even brew an espresso via the GHC; it just uses the profile you last selected. Having the machine function completely independently is a foundational safety requirement; the tablet is fully optional.
When the tablet is powered on, it actively tracks whatever is happening with the machine in real time. However, it does not mandate or lock the machine's actions, serving instead as a companion display to visualize the brewing process.
All data communications between the tablet and the espresso machine are completely wireless and function over a Bluetooth connection. The cable plugged into the mount is strictly for USB charging and does not handle data transfers. Because of this, you are free to use your own charger and mount or place the tablet elsewhere if you prefer.
While the tablet can be moved or used wirelessly, you should avoid letting the tablet's battery completely die on a regular basis. Just like with any standard tablet, letting the battery constantly drain to zero will ultimately shorten its overall battery life.