For me, the jury is still out on this one. Looking at it theoretically, it seems to me that it is a transfer between kinetic energy (speed and engine power) and potential energy (altitude). As energy can be neither created nor destroyed, it shouldn't make any difference which way you do it. However, practically, whenever I've done it, it always does actually seem to me to appear to be working, and you do seem to arrive at the target cruise IAS a bit more quickly if you do climb above the target altitude and then descend to pick up the target speed. I'm sure it can't be true, but it just always seems that way when you're doing it.
I think you've hit the nail on the head. When this came up elsewhere I did some very simple numerical integrations in the form of a spreadsheet...
Two aircraft with identical aerodynamics. Both aircraft climb at 55 m/s (just faster than min drag speed of 50 m/s) at an angle of about 2.5 degrees.
One aircraft gets to its chosen altitude and levels off. It accelerates to its cruise speed of 77 m/s. It reaches 65 m/s after about 30 s, 70 m/s after about a minute and is within 1 m/s of its cruise speed in a little over 2 mins.
The other continues the climb at 55 m/s for 20 s, so it gets about 50 m (150 ft) higher. It then pitches down and flies the reverse (2.5 deg downwards) for 20 s before levelling off. At that 40 s point, it's going about 1.8 m/s faster than the other aircraft. But it accelerates more slowly. After about 90 s, there's still a 0.6 m/s advantage in speed (about a knot and a half, probably the smallest noticeable increment that the step-believers would demonstrate).
And eventually, they reach the same speed of 77 m/s. The step is illusory, but the illusion persisted for a good while. The aircraft that performed the zoomy manoeuvre spent an extra 20 s in the climb at a lower speed. If you track the distances travelled, it never quite catches up with the one that simply levelled off.