Yes, ShipStation can send tracking information to your customers if you enable the shipment notification emails in the store's Notification settings and if your customer's email address is present on the order.
The ShipStation email notification option is turned off by default since most selling channels also send shipment notifications to your customers. ShipStation automatically notifies your selling channel when an order ships. This notification includes the tracking information as well, which your selling channel can pass on to your customer. However, you may instead want to use the ShipStation notifications so you can maintain control of all of your shipment notifications in one place and use the ShipStation notifications templates and customisation features.
For manual orders, you must add your customer's email address to the order. As long as the email address is present when you create the label, ShipStation can successfully send the shipment notification to your customer.
Amazon and certain other selling channels do not allow third-party apps like ShipStation to send email notifications directly to customers. For these selling channels, the email notification options will not be present in the store's Notifications settings.