No.
20 watts into 1 ohm will require 4.5 amps at 4.5 volts from the output of the regulated mod;
meanwhile the battery may be supplying the 20 watts as 5 amps at 4 volts.
I did specify battery vs mod.
so YES, not no.
the voltage output form a regulated mod is not the battery voltage. It is converted using a combination of Buck/boost and or PWM or pulsed DC circuitry to achieve the desired wattage.
At wattages requiring less than the battery voltage the mod will either regulate the voltage down or more often pulse the DC voltage on and off to get the desired wattage.
At wattages requiring a higher voltage than the battery voltage the ?Buck/Boost circuitry will boost the battery voltage up to get the desired wattage. this buck boost circuitry has some loss so it will use more watts from the battery than at a lower voltage output from the mod.
I am a lifelong Electronics tech and have designed Buck/boost circuits.
They all have some loss ie more watts in than out.