It can be separated. The additional power you apply pulling up still burns energy. You are not getting that additional power for nothing. If you are reducing your downstroke an equal amount it all evens out in terms of efficiency. You may be able to go longer and further in any given day because you are spreading the load but that is not an efficiency metric, that is a usage metric. That is pedaling effectiveness, your limit is not amount of energy available or burned, breathing, HR etc.. it is muscle fatigue. There are some studies that show although pulling up creates more power capability, there was no improvement and even a decrease in overall mechanical efficiency.

Not my study, I am just the messenger. I'm sure there are studies that may suggest otherwise.
http://www.radlabor.de/fileadmin/PDF...aefte_2008.pdf
that concept of efficiency and effectiveness clipped, unclipped, and pedal technique is littered thought the PDF and in the conclusion.

Firstly, shoe-pedal
interface did not influence the pedalling pattern during submaximal
cycling. Secondly, cyclists could change their technique by
actively pulling up during the recovery phase. However, doing
so impaired their mechanical efficiency.
Concerning the influence of the shoe-pedal interface, the lack of
difference between the pedals without toe-clips and clipless
pedals is somehow surprising. Indeed none of the kinetic quantities,
V˙ O2, NE and iEMG parameters showed any differences between
PED and CLIP, even for elite cyclists who are used to cycling
with clipless shoe-pedal systems.

Don't let someones study dictate what you feel. My pedal stroke and method is what it is and I'll ride on any given day until I don't feel like riding, maybe its my right leg, left knee, my nose running, I just felt like stopping, bored, I rode by a backyard BBQ and got a wiff of a steak and got hungry, my mind is elsewhere, I got a flat, who knows. It's never because I am pulling up or not that is impairing or helping.