You can! Just click on the “View progress” link after pushing a piece of content or open the “Content Cloud” tab (called “Content Repository” for on-premise customers). You can see the overall progress across all sites and also the progress per site in the Details list. If anything goes wrong, this tab will also let you know all the relevant details for debugging and solving the issue.
There’s even a central overview of all updates available in the “Synchronize Content” tab at the Content Sync settings pages. You can view all running updates, past updates, failed updates and even show the updates across all sites to always understand what’s happening.