Does ros::Duration::sleep spin?

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If I do ros::Duration::sleep does ros spin and are callback functions called?

No. Sleep just sleeps the thread for the specified duration.

If not is there a way to pause the program while still managing callbacks?

You can have a loop that alternates sleeping and spinning, as exemplified in this roscpp tutorial, or you can have separate spinner threads. I recommend reading the ROS wiki page on callbacks and spinning.