Started working at a bike shop during college and one of the first things roadies told me was they are indeed much more efficient because you can push AND pull on your pedals - generating a lot more power and making the ability to sustain that power a lot easier.
See https://www.bikeradar.com/advice/fitness-and-training/stop-p... for instance.
>Undertake your next few leg-speed intervals at the same cadence (such as 105rpm), but aim to remain more firmly planted in the saddle, with your pelvis acting as a foundation for your legs. This will allow you to maintain chain tension through the entire stroke, eliminating the ‘thud’ through the top and bottom of the stroke (the ‘dead zones’) as your chain loses contact with the freehub
Anyone who experiences what the author describes as "the thud" is pedalling so badly that almost anything they do to improve their stroke is going to be huge win. I'm not sure his advice is on point for people who already have reasonable pedalling technique.
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.