I structured my response so you'd have a clear understanding that the actual focal length number of 200 x 1.4 = 280mm because that affects 1) actual focal length and 2)the lens aperture. The thing is this: a 70-200mm lens with a 1.4x on it loses an f/stop of maximum light transmission, but is a 280mm lens; because it is only a 280mm lens, there is not "all that much" difference between what the 200mm shows and what the lens + converter shows...it is NOT the night and day difference many people might expect. if one takes that same 70-200 zoom and 1.4x converter pair and puts that on a full-frame body....the lens is STILL a 280mm focal length: it is not and never was a "360mm lens".
There is a great tendency to see the 70-200mm specification, and in some way, conjure up the idea that a 1.4x makes that into a "448mm lens"...it just does not work quite that way...the difference between a 70-200 with a 1.4x and a 350mm or 400mm prime lens is really a major, major difference. Because the body has its own built-in FOV factor of either 1.5x (Nikon,Pentax) or 1.6x (Canon), one gets used to the narowed field of view with any and all lenses; what REALLY MATTERS MOST is the actual, optical length of the lens, not the body's FOV factor.
When it really comes down to it, a prime 300mm f/4 lens feels and actually is, longer than the 70-200 + 1.4x, and a real 400mm telephoto lens feels, and is, much longer than a 300mm lens. When you put a "real" 400mm lens on a 1.5x camera, the effect is a very tight angle of view, with quite a high-magnification look to the images. The actual length of the lens, or a lens + an optical converter, is more-important in a practical sense than the body's FOV factor is.