Convert Firefox Extension to Web App

Hi, We have a Firefox Extension here: cashbackautomator.com. It works well, and people like it.? My questions is simple: can the functionality of this extension be converted into a simple web app? Here's what I envision: 1. People visit our site, and drag a link into their browser. Our web app becomes a part of their browser.? 2. When a person visits a site that is compatible with our product, our web app kicks in. It opens a small window on the users screen that lets them know they can save money.? 3. The user clicks the provided link, saves money, and the small window disappears.? The hard part of this program is whether a web application in a users browser can "read" what site the user is at, and alert the user when they are at a website that is compatible with our product.? Bottom line: I want to avoid the use of a download.