No. You should change your Photoshop setting back because you fundamentally didn't understand the setting you were changing.
The settings in Photoshop shouldn't be changed. EVER. They are the default settings used for creating a new blank canvas and nothing more. They are useful only in automated profile conversions. Photoshop will always work with the profile that it is given.
The place to change this setting is either the Lightroom export settings or Adobe CameraRAW import settings (bottom of the ACR screen). They will determine what colour profile your pictures are when the RAW files are opened in photoshop regardless of what you set in the photoshop settings. That is all about the working profile of the file.
Windows settings are on a device basis. They never deal with the working profiles in the images. There's only two possible correct settings for windows, sRGB IEC61966-2.1 or a colour profile you have created with calibration hardware specific for your monitor. If you have a wide gamut screen you should download the profile for your monitor from the manufacturer's website if you don't have a calibrator.
Photoshop will use the settings in windows to understand how colours should look on the screen. It will in realtime convert the colours from the working profile whatever they may be to the display profile set in windows. You can see this in the colour settings drop down as "Monitor RGB" will be whatever is set in windows.
Also understand that few systems understand colour profiles. Before you upload your images to the web, or give them to friends or send them to be printed you may need to use the Edit -> Convert to Profile tool to set the image back to sRGB or the colours will be all wrong at the other end. Also understand that you should never save a wide gamut image as a JPEG as JPEG doesn't have the bit-depth required to display all possible visually discernible shades of wider gamuts.