Hello BobvdMeij,
Technically the cloud processing is similar to the network processing - you enable the Cloud in the Network preferences dialog, then open the project and configure the batch process or run some processing operation. After that (if the operation supports processing on a cloud, for example, the export can be performed locally only) you'll be asked, if the operation should be processed in the cloud. Providing that you accept that, the data will be first synchronized with the cloud and then processed with the user-defined settings. After the operation is completed the project will be synchronized with the cloud again.
You do not need to have Metashape GUI opened while the cloud processing is in progress, but in order to synchronize the project with the cloud you need to open the same project in GUI again.
In terms of the processing time - it is hard to say, as some time will be spent for the data synchronization and it could be quite long in case of very large projects. So mostly this feature would might be helpful for those who cannot process the data locally due to hardware limitations.
Currently the cloud is working in test mode and is free for the Professional license owners. However, after the testing is finished the cloud processing would be likely converted to paid service with the plans configurable in the user's account on the Agisoft Cloud page.