Can returned items go back into my stock automatically?

Yes. On Plugins → Return Settings, open the Refund, Exchange or Cancel tab and tick Restock returned items, then click the save button on that tab (for example Save Refund).

Stock is added back when you complete the request in Orders → Returns, not when the customer first asks. It uses the returned quantity, or the full line if no quantity was set. Each tab has its own switch, so you could restock cancellations but not refunds for damaged goods.