I would like to present the user a loading indicator when a control is loading (some grids need a while to load - before even doing any data operation). Is there a way to display this indicator when caliburn.micro is initializing the control?

If you want to control the busy indicator from the viewmodels I think you should consider writing an "busy service" that you can inject into the viewmodels. Some ideas on how to do this are available here:

http://caliburnmicro.codeplex.com/discussions/221527

I might seem complex but basically it just looks upwards for the nearest busy indicator and turns it on or off.