Yes, you can reboot your device with ROOT. If you rooted with unrEVOked 3 before 3.21, your ROOT may not stay after reboot. Other methods should stay without problem.
Reboot: A simple reboot of your device. Turn off, turn on.
Recovery: A reboot into Recovery Mode allows for further features such as Backing up your device with a NANDROID Image. (a complete copy of your device incase something happens while you Flash ROMs or Kernels ext.) You can also Flash ROMs and Kernels from this Mode. As well as change a few settings if you know where to go.
Hope this answers your questions.
"Let the ROOT be with you!"