Does the current supplied to the load doubles when the voltage is doubled
It depends what the load is.

If the load is a resistor with good stability, and adequate power handling for the higher supply, then yes, at twice the voltage it will draw twice the current.

For other loads, the situation is more complicated.

If a resistor has a positive temperature coefficient, like a filament lamp, then it will take less than twice the current at twice the voltage, as it heats up and increases resistance.

If its power handling is only good for the lower supply, it may take twice the current briefly, then burn out and drop to zero.

More complicated loads, like a universal input voltage power brick, may take constant power when charging the laptop battery, so take twice the current at 120v that it takes at 240v.