Users can specify a Google Analytics profile for each extension. This will start tracking the extension's page in GA like it was its own site.
"You can also use Google Analytics to track the usage of your extension once it’s installed," says Google software engineer Qian Huang. "Check out this tutorial that explains how to integrate Google Analytics such that you can analyze how users interact with the features of your extensions."
Browser extensions can be a good way to keep customers engaged with your business, and being able to track that will no doubt help tremendously.