Currently, there are tooltips on the coordinates indicating when a model is loading, but it would have been nice it there was a separate tooltip always on display next to the Export button telling the user, whether the model is currently loading in or loaded.
You could use the existing Export service Get Export Connections or Runs API to see the progress of your exports. The actual interface for functionality would need to be implemented by the application itself. If you would like to see support for a specific Bentley product please submit an idea to the corresponding Bentley brand ideas portal.