Good grief! Why are you wasting our time with such things if you are not trying to actually use them?
Can a "magic box" be built to do this? Probably.
Can it be built according to your second diagram. Perhaps, but not as you show it.
Would anybody actually build it that way? Likely NOT! Except, perhaps yourself.
If you want a CONSTANT higher Voltage at V2, you are going to have to have something in there that is connected to the battery minus terminal. Notice, I did not call it GROUND. So, you are correct, you do not need an actual ground. But you do need a capacitor or something that is connected to the battery's negative terminal to hold that higher Voltage while the circuit, whatever circuit, goes about the job of creating it.
Your V2 is the Voltage across the load and the load is connected to the battery negative terminal. So that Voltage, by your own drawings, is referenced to that point. That point MUST be included in any circuitry that creates the higher Voltage you want. Otherwise that created Voltage is NOT referenced to YOUR own reference point and can not be said to have ANY VALUE with respect to it.
All Voltages are measured across TWO points, one of which is usually considered a common. And that common is often called "ground". That's just the way we talk and think about things.
I have wasted enough time on this.
As a crude switched capacitor booster demonstration, you can use a mechanical DPDT switch in order to flip the capacitor forwards and backwards. Make the capacitor large enough so that your fingers can move at reasonable speed. Hey presto! No electrical ground for the controller!
Yes reversing the capacitor polarity works also if you do not want V2 to be 3x V1
I'm not interested in building this just want people to understand that a "magic box" with just two wires connected, in series with the load and no connection to ground can start with zero energy and can have V2 >> V1 for short periods of time proportional with the amount stored in the capacitor and inversely proportional with the load current.
I should have added also a small capacitor in parallel with the 100Ohm to show that V2 increases to somewhere close to 30V then decreases well below 10V before another cycle can be repeated and it is not possible to maintain 20 or 30V at V2