Do internal noise like thermal noise in a system extract power from the DC supply?
The theoretical answer would be NO.

For example, the thermally induced noise in the following circuit will not be drawn from the power supply:







simulate this circuit &ndash; Schematic created using CircuitLab

In fact, you can measure a thermal noise even this way:







simulate this circuit

However, it is rarely the case in modern circuits that the internally generated noise is not amplified. For example, in the following circuit the thermal noise of the resistor R can cause a power to be drawn from the power supply:







simulate this circuit

Therefore the complete answer would be: it depends on the circuit in question.