More important than simply diving for speed, is finding the best acceleration AOA for that aircraft. This applies not only to jets, but to all aircraft. Unfortunately the only example I have is for the F-15...
The best acceleration for that plane due to it's wing, is at a positive AOA. That means that at low speeds, it accelerates best below 1 G, and at higher speeds, it actually accelerates best above 1 G. Engine design (more efficient at low altitudes?), prop design (number of blades, length, pitch, twist, chord and aspect ratio, tip shape), engine thrust line, wing and stab angle of incidence, wing camber and airfoil shape, tail camber, amount of parasite drag, even surface texture, all affect how the plane performs at different speeds.
One definate benefit of diving after a running enemy is that for a while, you will be accelerating faster because at the lower G in the dive, you have lower induced drag. Similiar efficiencies can be seen in climbs due to part of the engine's thrust being used to cause the climb in addition to the wing's lift. This is why the best fuel efficient profile is a best-rate climb to near max altitude followed by a high alt cruise, followed by an idle power descent.
Lots of stuff works that isn't very obvious, and it's different for each plane.
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eagl <squealing Pigs> BYA
Oink Oink To War!!!