Not really. Kaitenage is actually quite different than a whizzer. First off, kaitenage is an underhook on a person's arm, while a whizzer is an overhook. Kaitenage is focused on control near the elbow joint while the higher a whizzer is, the better.
Also, no, kaitenage is not a good defense in relation to a single leg or a double leg take down. I'm not sure how popular it is in Australia, but go to any high school wrestling team here in the States and try kaitenage while someone shoots in on you will be repeatedly hitting the mat.
I would say that the arm movement of kaiten, in tha particular instance would be like a "bras à la volée" xommon in catch as catch can, free wrestling and so on.
And if it is the only thing you try do do with katien, well it has almost no chance to succede against a shoot.
But from my limited understanding that is not a proper kaiten either . we are missing the control of the head. Even in "normal" aikido situation if you do not tuck the head toward his chest, he can walk of the throw, he will not have a reason to break fall at all.
Let alone in the case of a shoot where if we do not compromise his structure (or base), we will go splat as he will destroy ours either by tankig our knee or our hips.
In fact controlling the head and in such manner and moving a leg back, is the medieval wrestling response to a shoot and SLT/DLT
The only modification to kaiten is you control the head before the arm.