MS does not distribute updates through web browser popups. Windows OS and application security updates are handled by Windows Update (at least since XP) and updates to Microsoft applications not distributed this way require you to go to a Microsoft website.
Although Windows includes many generic drivers for broad classes of hardware, Microsoft does not distribute these in browser popups. Most device-specific drivers are distributed by hardware manufacturers. Windows might search for a driver when new hardware is installed, but updates for these are also not pushed by browser popups.
Browsers may notify of the need for updates to plug-ins (Flash particularly) or system services (e.g. Direct X, .NET Framework, Silverlight, Visual C++ distributables) when you go to a website that wants a newer version. These are not really drivers, and most of the time the system services updates are pushed by Windows update, or you get notification when trying to install a new application that needs a newer version.