I use clip ins now, have for about 5-6 years.
I don't think you actually pull up.
The pulling up of your leg results in easier pedaling overall, and it is relatively as if you are pulling up on the pedal. Should you actually then pull up? You should go for the most natural sustainable pedal motion for you. When I pedal I "visualize" my feet going in circles, not up and down, it helps me on the "over the top" and "across the bottom" parts of the circle. keeps me sinusoidal!
If you never pull up at all and you are pedaling and feeling tired, try pulling enough to remove the dead weight leg from the equation and you'll feel rejuvenated.
It's also quite noticeable when you switch to clipless and go for a hard ride, suddenly new muscles will be sore.
you should try it, you can feel the relief in the pushing leg.