Yes, ShipStation can send tracking information to your customers if you enable the shipment notification emails in the store's Notification settings.
This option is 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 want to use ShipStation's notifications instead so you can maintain control of all of your shipment notifications in one place and use ShipStation's notifications templates and customization features.