Checking that Google Analytics plugin is completely asynchronous

The plugin uses the exact code recommended by Google in their official docs. The best way to analyze the added scripts would be to take a look at the source code of your pages and take a look. You also could run your pages thru various free online performance checkers, that would give you more information about how the scripts are loading, whether there is any blockage, etc.

That in mind, about your concerns:

“I’ve always assumed that the javascript used in Google Analytics completely asynchronous. That it takes virtually no time to execute and that it can’t “hang” if (for example) there’s no communication path to the receiver.”

Correct. The only thing this plugin does is output a bit of code to your web pages. It isn’t “phoning home” or anywhere else. It simply grabs the GA plugin options from the database and outputs the required code as needed.

“I’m just going through all my plugins and trying to determine if there’s one that could potentially hang if some network path is down.”

Same thing as previous reply, there is nothing in the plugin that would cause this to happen.

I hope this helps, let me know if I can provide any further infos.