No. Hyrdostatic shock is dependent on tissue density but regardless, most tissue is too elastic to receive permanent damage from these forces in ANY projectile traveling under 2000 fps. This is not conjecture or supposition, but demonstrated and observable fact.
This is relative. Without cavitation, only the permanent wound channel being physically displaced by the projectile actually damages tissue. This means that your wound channel is usually approximately the size of the projectile, or a little less depending on the bullet's profile. So yeah, at 250 yards, your typical 125 gr x39 load has between 1600 and 1800 fps. At this velocity, it may show some expansion, but probably isn't going to expand past .45 caliber. So your wound channel, and yes, I have shot game at this range with a Yugo SKS, is going to be about half an inch in diameter. Generally speaking, this is plenty big to be unpleasant, but a similar bullet in a 5.56 is likely to create a wound channel several orders of magnitude larger because it still has over 2200 fps at that range with most loads. This means the bullet not only expands more, but this expansion causes more hydrostatic shock damage.
The same could be said of a 5.56 round. Getting shot sucks.
Yaw is not dependent on velocity. All spitzer (pointed) bullets have a tendency to yaw in mediums more dense than air because their center of gravity is located more towards the rear or base. Projectiles naturally want to fly mass forward, so all pointed bullets want to flip or yaw and fly base forward. This is not as dependent on linear velocity as much as rotational velocity. The primary wounding mechanism of all military pattern FMJ rifle bullets is yawing. This includes the 7.62x39 and is why the later M67 pattern projectiles are so much more effective than the earlier M43 projectiles. Fragmentation is velocity dependent. Both the M193 and M855 require 2500-2700 fps to reliably fragment, and most 5.56 mm rifles will reach this velocity around 140 to 180 yards.
I don't know how much simpler I can say this--beyond 120 yards or so, the wound capacity of the 5.56 is significantly greater than the 7.62x39.
Now then, whatever happened to "most humans or thin-skinned and weak...?" There is a prevailing myth that the 5.56 was designed to wound because the theory is that a wounded man takes more resources to deal with than a dead one. This is false. The 5.56 was not designed to wound rather than to kill. It was designed to wound rather than to miss. Hitting with the 7.62x39 beyond a couple hundred yards takes a lot of skill and practice. The 5.56 can easily hit to well beyond the distance it is actually effective by most standards. Now then, each of these hits may not be the Hammer of Thor, but even with the effect of being stabbed by a foot long screwdriver from say, 500 yards away, where the 5.56mm M855 has about the same velocity as the 7.62x39's 125 gr load has at 250 yards--1600 to 1800 fps--most humans are thin skinned and weak, and so this constitutes still a very bad day, does it not? And if a basically trained Marine can do this regularly while poorly trained conscripts and disgruntled goat farmers are missing with their AKMs, that makes the 5.56 more effective at that range, does it not? And that is with military issue ball ammo. In the civilian sector, the heavier 70+ gr OTM and monolithic expanding hollow points will be more effective at 300 yards than anything you can load in an AK will be at half that range because the 5.56 carries enough velocity to kill like a rifle at that range whereas the 7.62x39 is a SMG round beyond 150 yards.
At any rate, caliber wars have been done before. Fackler and his decades of research in the field of terminal ballistics is available online for free with a simple Google search to anyone who cares enough to look. And it is not my intent to hijack the thread, so I am done with this aspect of the discussion.