Assuming you properly calibrated and profiled the monitor to D65 with the computer's GPU set to output to a D65 monitor it should.
Photoshop doesn't really take your monitor profile into account. But it doesn't have to because Photoshop isn't what displays your image: Your GPU and monitor do that. Photoshop outputs the image to your GPU in much the same way it outputs images when you export them to a file. It includes instructions regarding the proper color space along with the numerical values for the image and then the GPU translates that to the correct color levels to send to the monitor.