Very well asked question. Here is my take on long zooms;
The simple answer is, "it depends on the lens AND the camera." Which doesn't answer anything but it does give a hint to the overall way lenses can work, which is all over the place. Some are better (quicker) at finding and picking the focus point, some less so. Whether you have an expensive lens or an inexpensive one, the physics behind what is required are the same.
First you must understand that the construction of a multi-element lens is very complex. A lot of the interior lens elements need to shift around in order to get an image into focus. With a variable zoom lens, the action is compounded because all those elements need to be able to focus throughout the entirety of the focal range of the lens. For a 70mm lens the action can be pretty simple since the focal range doesn't change. With, let's say a 70-200mm lens, the elements must be able to focus at 70mm, at 200mm and at every step of the way in between.
Using your example, when you are focused on something near you at 70mm, all the elements are positioned to bring that subject into focus. Once focus is captured it doesn't take the lens too much effort to go from 70mm to 100mm because the internal elements may not need to shift a great deal. All that is changing is the field of view. However, when you bring the camera up to the deer in the distance and you want to zoom in, both the field of view AND the focal plane need to shift internally. Here is where different systems handle the task differently.
Most cameras use contrast to find focus, meaning it looks for 'contrasting edges' either with light or color, and uses that as a guide to gain focus. The more focus points a camera has the better it may be at finding focus. There are also two types of focus points, vertical line sensors and cross (vertical and horizontal) line sensors to detect that contrast. Cross types work best. The quicker the camera can detect that local contrast on a focus point the quicker it can gain focus.
Understanding that, the solution to your problem is dependant on your given situation. If your camera has only a few points of focus and if you have only a few cross type focus points (which is common in less expensive and older cameras) you will have a hard time gaining fast focus. Also, if you point at your subject and there is not enough contrast on a focus point your camera will have trouble and will 'hunt' to find focus. To get around this, yes, manually getting the subject into relative focus by hand as you go from one extreme to the other will help immensely. Also, placing your focus point(s) on something with contrast also helps the lens gain focus. For example, if you have nine focus points and only the center point is cross type and you place that on the body of the deer... a smoothly textured, evenly colored body of a deer with little contrast, the lens will likely have trouble gaining fast focus. Place that center spot at the edge of, for example, a white spot or black of an eye and your chances of finding focus increases exponentially.
Hope these tips help.
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