When printing a grayscale image it's treated exactly like the black channel of a color image. So in order to get a correct preview of how it will look on print it must be soft proofed with the CMYK color profile the printer recommends.
InDesign does this by default. If I place a grayscale image in InDesign the image will be mapped to black ink by default. When I turn on View > Proof Colors set to the correct color profile, I get a realistic (and often slightly depressing) preview of how the image will look on print when printed with black ink:
If I open the grayscale image in Photoshop it's shown as if it were a neutral RGB image:
The darkest point is RGB(0, 0, 0) and the lightest point is RGB(255, 255, 255). So I can't trust that the image will look like this on print.
In Photoshop I can also turn on View > Proof Colors with the same settings as in InDesign, but then the image is shown as if it was converted to CMYK. It is slightly darker and (with this specific color profile) more neutral as it uses all four CMYK inks to create the image:
Photoshop doesn't seem to know that I want to see the grayscale images as it would look if printed in only black ink. Actually the preview looks exactly the same as it would with a neutral RGB image.
I can hack my way to get a proper preview in Photoshop if I create a CMYK image with the correct color profile and paste in the grayscale image in the black channel:
But that isn't a practical way to work for multiple reasons.
Is there a way to properly soft proof grayscale images in Photoshop taking the ICC profile into account?