Does MageMail track the website browsing activity?

No, we don't track things like page views.  

There are a few client-side things that we do, such as detecting the email address when they type it in during checkout. The bulk of the data that we use for triggered emails comes from the Magento database - whether from newsletter signups, orders, quotes, customer records, wishlist records, etc.

One of the benefits of this approach is that we can tie into actions that take place via the Magento backend (phone orders, etc.), which wouldn't be tracked via a frontend cookie.