My Mac's screenshot colors were off and I was terribly confused. I found this question and started investigating.
Summary
Use the display color profile sRGB IEC61966-2.1
when you want to take screenshots.
How I debugged it
I created an image using GIMP that had a section of yellow RGB(255, 255, 0) and inspected it with the "Digital Color Meter" MacOS app. I thought the Chrome browser's color picker was acting kind of strange so avoided it.

Notice 3 things:
- On the left, the color information of the file is not present.
- Top right, you see the color meter show RGB(255, 255, 0). This is the color value that will end up in your screenshot file.
- On the bottom, the monitor profile is set to sRGB IEC61966-2.1. This was the only profile that I found gave me accurate screenshots.
Compare that with the readings when I activate other color profiles. The following Color LCD
profile shows RGB(255, 253, 84) on the color meter. This was the default color profile, and although it might not be obvious on your screen, on mine it made the strong yellows look whiter, more like a banana. The worst part was that I just couldn't figure out which colors were the underlying real colors by analyzing screenshots.

The Generic RGB profile shows RGB(255, 255, 11) on the color meter.

Answering the original question
I believe the answer is no, though you could develop a method. You can't have a color profile and take non-color-corrected screenshots. Looking at the MacOS APIs for capturing the screen:
There doesn't seem to be a parameter that would allow ignoring the display color correction. What you could do is implement a tool that:
- Sets the color profile to sRGB IEC61966-2.1 by using
CMSetSystemProfile
- Takes a screenshot
- Then sets the profile back to whatever color profile was active earlier.
Also, there might be other APIs I'm unaware of.
Here's my original test png:

Image embedded color profiles complicate things
If I take a screenshot when the Color LCD
profile is active, the Color LCD
profile is saved in the screenshot metadata. So even when I open that screenshot later when the sRGB IEC61966-2.1
profile is active, it's only slightly color-distorted to RGB(254, 255, 0), but some apps disregard the attached color profile, like the website photopea.com which will cause dramatically incorrect colors RGB(255, 254, 84).
This investigation was really confusing. Hopefully folks that read this get slightly less confused.
