Not so quick, please.
In its simplest form usual display profile consists of two parts.
One is gamma correction graph, which is loaded into graphic card/driver LUT and is not directly detectable by screen color-picker (does not change its readings).
Another part is screen color model - mostly color primaries (RGB coordinates in some profile connection space), this the basis of software color correction - and this already changes underlying pixel values, sent to the driver and graphic card and affects color-picker readout.
It is rare for real screens its primaries to match precisely to sRGB or Adobe RGB or some other common color space ones, thereby (if any custom profile is in use) pixel values usually do not match image values. For monitors with hardware calibration this can be achieved - at least for smaller color spaces (like sRGB on Adobe RGB capable monitor); for common consumer monitors almost never.
Of course displaying non-native color space images (like AdobeRGB ones on even hardware-calibrated sRGB screen or vice versa) yields profile conversion in viewer program, which may change pixel values in different ways, depend on color management system properties and configuration.