If you download and install the AJAX email example: (VB) / (C#)

It has this line so that the module will delay enough for the progress bar to appear:

'Sleep so that you can see the progress indicator - remove when in production
System.Threading.Thread.Sleep(1000)

When you test this using the default skin that comes with DotNetNuke, it should work. 

Yes

Here is the "rule of thumb" that I use. If I have more than one independent section I need to update I must NOT use the "Supports Partial Rendering" and I must do use Update Panels that I place in the module myself.

For example, with the AJAX Email Module example,

You search for a person and it updates a grid, then you select from that grid and it updates another. In this case you have to do the Update Panels manually. Mostly because you need to indicate the triggers that will be used to determine when to perform the update for each panel. Also it allows you to NOT update the panel in the other situations.

I have used ASP.NET AJAX extensively with DotNetNuke for very large projects. Using controls from the AJAX Control Toolkit (see:Using the ASP.NET AJAX Control Toolkit) is practically a requirement at this point. Controls like masked edit are vital in a business application.

I find that each module "page" presents unique challenges. I find that I can usually only use "Supports Partial Rendering" on a simple module "page". On a large module page I usually only want a small section to be updated.