The answer to whether or not a pull-up resistor consumes power depends on whether or not current flows through the resistor.
If the pull-up resistor is used to hold an input to a logic high level, and the input pin merely drives the gate of a MOSFET, the current through the resistor will be negligible.
The same applies to most MOSFET gpio pins configured as inputs.
BJT inputs, however, generally draw current.
If the pull-up resistor is used to pull up a pin that can also be driven low by some other device, such as a manual switch connected to ground, or an open collector or open drain output, then the pull-up resistor will consume power when the output is low.