Yes, you can track time to two different cases using two different browsers.

e.g: If the auto timer is enabled on the Cases object and you have opened different cases on two browsers (Chrome and Firefox Browsers)

The time is tracked for both cases at the same time.

There are two types of auto tracking that can be configured in your org "Separate" and "Restart". Click here to know more.

Note: The time is tracked separately even if you have set the configuration to Restart for the auto-tracking if you are tracking time on a different browser.