Yes sleeping does help broken bones heal.
When you sleep your body goes into recharge mode and your body including your bones heal as you sleep.
Sleep is very important to healing bones and sleep is very important for your overall health.
If you have broken bones the best thing you can do is avoid straining the broken bones and if possible get a lot of rest.
Sleep more often and you'll notice your bones healing faster and you'll be much less tired as well.
If you break your bones it can be hard to do anything anyway so sleeping is a good thing to do to help your broken bones heal up.
Just like when you have a cold or flu virus you recover much faster if you rest and sleep as sleep helps our bodies heal and repair itself.