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Springle,

I suspect it all comes down to the tried and true rule of thumb in the non IS/VR days of using at least 1/(effective focal length) shutter speed to ensure camera shake does not result in a blurry image.

Like binoculars when viewing through a lense with a higher magnification any shake is amplified more or less linearly (not the square of the distance as one might suppose) with the distance to the object due to the progressively more narrow field of view of Telephoto lenses as the focal length increases.

A smaller sensor results in a narrower field of view as the image sensor gets less of the image circle of the lens. Likewise a teleconverter increases the focal length.

The shake is an angular momentum perpendicular to the axis of the lens. If you draw it out this angular momentum is a right-angle triangle with the long axis along the focal point and the short axis in the plane of focus. The longer the effective distance the faster shutter speed required as the effective length along the plane of focus increases.
 

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The question remains: Will, for example, the 70 mm - 200 mm F2.8 IS lens yield the same stop gain for a 5D II as it would for a 7D? Or suppose I attach a 5D II to this lens, along with a 1.4 teleconverter. Do I obtain the same stop gain with the teleconverter as I would without the teleconverter?
Yes.
As you are shooting at a longer focal length with the converter and you will have a light loss (exposure factor) with the teleconvertor you will get the same stop gain but as you lose 1 -1.5 stops with the teleconverter your effective stop gain will be less.
WRT Rules Of Thumb, consider the following. I have an old non-IS 70 - 200 F2.8 lens. I don't recall its metrics, but suppose it weighs 20 ounces. I also have a non-IS 200 mm F1.8 which weighs around 100 ounces. Which lens do you think I'd be better able to hand hold (at 200 mm)? Or would photos shot at 1/200th second show the same sharpness, certes paribus?
You could argue that the heavier lens would make you more stable (dampening) or vice versa but those 200mm f/1.8 or f/2 lenses are, indeed, bricks and really throw the balance off as their weight is so more than the body. I guess that's why most people would use a monopod with a Wimberly gimbal mount
And who would try to hand hold a 600 mm F4.0 at 1/600th and expect sharp photos?
An NFL linebacker who isn't using Steroids?
 
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