No this is not correct.
Look at figure 2.6 “vertex transformation sequence”, page 41, OpenGL spec 2.1.
gl_Position are the clip coordinates of the vertex.
From the clip coordinates, you first have to get the normalized coordinates with a perspective division:
Then apply the viewport transformation (section 2.11.1 controlling viewport, page 42)
vec2 lowerLeft; // lower left corner of the viewport, given
vec2 o; // center of the viewport, computed
// From end of page 42:
vec3 win // window coordinates of the point
// from section 2.11.1
// we don’t care about win.z for this computation
Then, because you are looking for point coordinates, you have to refer to “section 3.3.1 Basic Point Rasterization”, page 97.
“In the default state, a point is rasterized by truncating its x_w and y_w coordinates (…) to integer.”
So the operation is not round(), floor() or ceil() but truncate, so it is just a matter of casting a “float” into an “int”.
As a side note, chapter 3, page 90, remember that a fragment is a grid box (assumed square), located by its lowerleft corner, which lies on integer grid coordinates. The fragment’s center is offset by (1/2,1/2) from its lower left corner, and so lies on half-integer coordinates.