No that is not correct. If I have say a 28-105 lens that has an aperture of 3.5-5.6, the 1.4x converter will work at ANY focal length as the max aperture of f3.5 + the 1 stop of light loss = f5
At 105mm the lens may still show an aperture of f8 but AF will still function as the max aperture of the lens is still f3.5. In a constant-aperture zoom, the diaphragm opening is either effectively opened wider or closed down narrower as one zooms to longer and shorter focal lengths - this extra engineering is necessary to try to maintain a constant aperture. Since the aperture of a lens, in f-stops, is equal to focal length divided by iris opening, longer focal lengths require wider openings and shorter lengths require smaller openings to maintain the same ratio.
However, in a variable-aperture zoom, the designer simply lets the iris opening stay fixed during focal length changes (or sometimes only partially compensates for focal length changes). If the diaphragm opening is fixed at a certain size, as an example, then zooming to a longer focal length will result in a larger f-stop ratio (i.e., a smaller aperture), while zooming to a shorter focal length will result in a smaller f-stop ratio (i.e., a larger aperture), even if the aperture ring is untouched by the photographer.
Few experienced togs call it the f/number. It's generally referred to as the aperture (or f-stop) - the size of the lens opening.
We're maybe splitting hairs though AND we're off topic