Hi Dan Kristian,
Theoretically, if you have the application file of the browser (*.apk), you can add it to the list of TestComplete's TestedApp objects so that TestComplete instruments the app. After this, all objects should be recognized by TestComplete. However, this won't work for the browsers installed on devices by default. We have a suggestion in our DB to improve the web testing on mobile devices - I've increased its rating based on your request.
At the moment, TestComplete provides the Virtual Browser feature. It allows you to emulate a mobile browser on your desktop. Please refer to the
"Testing Mobile Web Applications" article for details.