No, not as soon as orders are placed. However, most store integrations include a setting to allow ShipStation to refresh your stores automatically while you are away. If you have enabled this option in your store's settings, ShipStation will call the selling channel to request orders if a certain amount of time has passed since the store's previous update.
This option is located in each store's Store Settings tab.
This option is enabled by default for most stores and can be disabled if you do not wish for ShipStation to import orders for that store automatically.
To ensure you are always working with the most recent order information in ShipStation, click the import button 
in your ShipStation toolbar. You can initiate an order import for all your stores at once, or any individual store you select.
At this time, automatic imports cannot be scheduled or customized.
Auto-update Not Available for All Stores
If your Store Settings does not display the option to Allow ShipStation to refresh your stores while you are away, this means the auto-update option is not available for that store. Use the import button to import orders instead.