The "pulling up" effect is often over exaggerated; the vast majority of your power is generated on your downstroke. The real benefit of clipless pedals are the fact that it forces you to use cycling specific shoes. Many people use running shoes or whatever they can find under their bed and often these soft sole shoes have very poor power transfer, meaning that the force you apply is often absorbed by the shoes instead of being transferred to the drive train.

The other benefit of clipless is that it provides foot retention- in very aggressive riding situations when you need to apply a lot of torque your feet may slip off the pedal. This can also happen if you are riding in wet weather and your platform becomes slippery.

There are benefits to "pulling up", as it engages different muscle groups (mainly calves) and with experience you will learn how to distribute the load. You won't generate significantly more power, but the load will be distributed more equitably. The best way to learn this is to practice one-legged drills: find a park or a quite road and just pedal with only one foot clipped in. You'll find that in order to avoid being fatigued too quickly you need to distribute the load throughout the pedal revolution.