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.

I think my monitor calibration is OK, so I will assume my monitor is displaying D50/2 Lab values. If I calibrate it to a 5000K white point, will the display of the D50/2 Lab values be more accurate?

If you calibrate it to D50, which is a little bit greener on the Green←→Magenta axis than a blackbody radiator at 5000K, they will. But only if your ambient lighting is also compliant with D50!

Keep in mind that our perception of what is white changes with the environmental light. If you are in an environment with light centered on 5000K and you have your monitor set to D65, "pure" white will look slightly blue to your eyes. Only when the ambient lighting is also D65 will pure white on the monitor look white to your eyes. Conversely, if your monitor is set to D50 and your ambient lighting is at D65, "pure" white on your screen will have a red/orange/amber tint to your eyes.