Yeah you do!

Read up more on gymnastics websites or the like before you attempt then though. Don't want to go straight in and get injuries. I believe there'll be progressions for you to work up to false grip. Like maybe you just do hangs for some number is seconds and build up the time slowly.

All the best

With regard to pull ups specifically, look up false grip pull ups. It's a higher level skill than regular pull ups, but it's pretty much exactly what you described: curling your wrist over the bar. Do it with both hands/wrists and your elbows will be the same height.

You can also try using gymnastics rings for this as it might be easier.