Hunter - the lens takes that extra 1/2 second searching for focus.
You want to point your camera ( and focus point ) on your target, half tap the shutter button and have that fucker hit focus instantaneously.
Yes, but this is also contingent upon good body/lens compatibility and using the right AF mode in your body. I am not familiar with Nikon, but in the Canon world you would want to use "AI Servo" AF, which senses motion towards/away from the photographer, and adjusts the focus distance accordingly as the photo is being taken. If a motorcycle is coming towards you at 150mph and you hit the shutter halfway to AF, then click it all the way to snap the shot, your shot will be out of focus if you're on the wrong AF mode.
But yes, focus hunting can be killer. It is more often experienced with 3rd party lenses.
OP, see if you can find, borrow, or rent a 300mm f/4.0. That ought to give you the combo of length, quality, and AF speed that you need, while costing $1350 new. Still pretty pricy, but less than half the amount of a 300/2.8, and better reach than a 70-200/2.8.
Or you can buy a 70-200/2.8 and a 1.4x teleconverter to make it into a 100-280mm f/4.0. Which would give you a little more versatility, although it would lower the image quality and AF a little bit, but still it would kill any consumer-level zoom.