Can I use a grayscale image with the OpenGL glTexImage2D function?

Change it to GL_LUMINANCE. See https://www.khronos.org/registry/OpenGL-Refpages/gl4/html/glTexImage2D.xhtml

in the FragmentShader, you can write:

uniform sampler2D A;
vec3 result = vec3(texture(A, TexCoord).r);

in the cpp file,you can write:

glTexImage2D(
    GL_TEXTURE_2D, 0, GL_RED,
    dicomImage->GetColumns(), dicomImage->GetRows(),
    0, GL_RED, GL_UNSIGNED_BYTE, pixelArrayPtr);