If I move an order back from Shipped to Processing, does anything get undone?

Very little. Pick Processing in the status dropdown and click Update Status. The status changes and the move is added to the Timeline, but:

• Stock isn't touched, because it's still reserved for the order.
• No push notification is sent. Those only go out for Shipped, Delivered and Ready for Pickup, so the earlier "shipped" notification can't be taken back. One exception: if WhatsApp Notification is on with the Order Confirmed message enabled, moving to Processing sends the customer that message.
• The carrier and tracking number you saved stay on the order. While they're there, the Fulfilment column (turn it on with Columns) still says Shipped, and the customer's Track your order page still ticks the Shipped step.

When the parcel really leaves, set the status to Shipped again. If you want the customer to know about the delay, tell them directly and record it with Add note.