For the lines in the X-ray spectrum, yes. Moseley also correlated the L-alpha lines belonging to the L-series of the spectrum with atomic number and found good correlation. The L-alpha series represents the transition from a level 3 orbital to a level 2 orbital. The L-alpha lines are not as intense as the K-alpha lines.
Section 2.2 of the following paper explains very well how X-ray techniques were used to determine Z. It is a good read, and shows the correlation lines between the frequency and atomic number: http://www.spectroscopynow.com/FCKeditor/UserFiles/File/specNOW/Enc_Anal_Chem_6801.pdf
BTW, this kind of X-ray radiation coming from the movement of electrons between energy levels is called "characteristic" radiation (because each element would have peaks "characteristic" to that element). There is another kind of X-ray radiation, called "continuous", "white radiation", or "bremsstrahlung" radiation. When electrons are fired to a metal target (they are fired by using a difference in voltage), they decelerate. This deceleration emits energy in the form of X-rays if the original source is of high energy. Hence, white radiation does not arise from electronic transitions between energy levels, but from the reduction in the speed of electrons as they hit the metal. Continuous radiation is not correlated to Z, only to the accelerating potential of the electrons. Hence in theory, two different elements (different Z) should have similar continuous radiation spectrum if their electrons were accelerated to the target using the same high voltage. Their characteristic spectrum, however, will be different.
Notice that Moseley did not derive his equation based on theory. He used the results of his experiments to find a relationship between frequency and Z. Once he had that, he went to the Bohr model (which was the existing atomic model accepted at the time) and attempted (successfully) to correlate this relationship with what was known (or theorized) about electronic transitions at the time. So Moseley's relationships are empirical, but the results could be explained by the Bohr model of the atom.
Unfortunately, introductory chemistry books don't explain this very well. In my opinion, physics books are much better at explaining all of this, even though this has lots of implications in chemistry.
I hope this helps.