No, this is not the case. Aperture F stops are calculated on pupil size and focal length of the lens.

From wikipedia

In optics, the f-number (sometimes called focal ratio, f-ratio, f-stop, or relative aperture1) of an optical system is the ratio of the lens's focal length to the diameter of the entrance pupil.2 It is a dimensionless number that is a quantitative measure of lens speed, and an important concept in photography.

Whereas a T-Stop is a measured unit and lenses set at the same T-Stops will make the same exposure.

More, from wiki

A T-stop (for Transmission-stops) is an f-number adjusted to account for light transmission efficiency. A lens with a T-stop of N projects an image of the same brightness as an ideal lens with 100% transmission and an f-number of N. For example, an f/2.0 lens with light transmission efficiency of 75% has a T-stop of 2.3. Since real lenses have transmission efficiencies of less than 100%, a lens's T-stop is always greater than its f-number.[6] Lens light transmission efficiencies of 60%-90% are typical,[7] so T-stops are sometimes used instead of f-numbers to more accurately determine exposure.[8] T-stops are often used in cinematography, where many images are seen in rapid succession and even small changes in exposure will be noticeable. Cinema camera lenses are typically calibrated in T-stops instead of F-numbers. In still photography, without the need for rigorous consistency of all lenses and cameras used, slight differences in exposure are less important.