Umm... it's a bit different how ICC profiles are used by the OS.
A display profile defines the characteristics of the display device: what are its primaries, white point, black point, etc. The display profile must be associated with your display device in the Windows Color Management application (press Start -> start typing Color Management) by having it in the list for the device and having "Use my settings for this device" enabled. The OS does nothing after you associate that profile (*), it does not alter the color rendering of applications. It's the responsibility of an application to do something based on it. That "do something" means the application will use either the color transforms provided by the Windows API or by some other color engine (like little CMS) to transform its RGB values to new RGB values which would give the desired human color perception on this display device.
Some of the Microsoft applications that come with Windows do make use of color profiles to change the colors of their output. Others do not. The Windows OS doesn't do anything by itself to applications (at least not to Win32 apps).
Now, there's a catch, related to my (*) in the statement above. ICC profiles allow to store gamma correction for the three primary colors in their VCGT (video card gamma table) tag. If a profile with this tag info present is associated with your display device and you have "Use my settings for this device" enabled, then Windows will use that info to load modified gamma ramps in the gamma tables of your graphics card. This means that indeed, in this case, there is a correction applied by the Windows OS itself that affects the color rendering of everything your video card outputs: of the Windows desktop and of applications.
It's not a "complete" correction, because in order to have a complete correction you need colors to be remapped too (from the gamut used by an application, like sRGB, to the actual gamut of your display device, according to a desired rendering intent). The color correction provided by the loaded gamma tables affects all colors indeed, but guarantees only neutral grays to show the right way (it's a "grayscale" correction). What does it mean the neutral grays are perceived the right way? It means they appear neutral (not with a reddish or greenish or blueish tint) and the luminosity is the right luminosity for a given gray level.
How close the other colors are to the desired rendering after this gamma correction depends on the characteristics of the display (how linear the display characteristic is, and they're usually not linear, etc).
The precision of these gamma ramps is also limited.
Some applications, notably games, will reset the info loaded in the video card gamma tables to unity when they start, which means neither those games nor anything else on the Windows desktop is color corrected anymore. Windows may or may not re-load the corrections after that application ends. There are other cases when Windows doesn't reload the graphic card gamma tables from the VCGT tag of the color profile, which is why color profiling apps such as DisplayCal come with their own tool that runs in the background (the DisplayCal app has its icon is in the taskbar) to reload the gamma tables from the profile VCGT tag to the graphic card from time to time.
The best way to have a calibrated display device, is to have a device that allows to upload a 3D LUT to them (like the LG OLED TVs). A 3D LUT allows to correct nonlinearities anywhere in the color volume (a "volumetric" correction) that corrects all colors, not only the neutral grays.