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've done kaiten nage myself and seen a variant used in BJJ matches (in response to a leg shoot). Agreed that it's not like a whizzer. When used effectively in a grappling environment - it's much more like a three-quarter nelson, in that you're controlling the head and spine by breaking the structure of the other guy via your connection to him.
It's usually not the big projecting throw as seen in aikido demos, but more of a forced roll onto the back (good opening for side control unless the guy has a killer guard). Depending on the competition rules against neck/spine cranks it isn't always allowed. The thing is - you have to sprawl first.
If you don't know how to sprawl (or pass block from football, which kickboxer Maurice Smith used very effectively against Mark Coleman in the early UFCs, musta been all them grass drills), then a good leg shoot is going to give you lots of problems as it 1) often causes someone unused to it to bend over - breaking their own structure and allowing the opening for kuzushi/off-balancing 2) the incoming force then whips that person back the other direction, which is what capitalizes on the off-balancing and causes the takedown.
The good news is that a lot of aikido folks already have a sprawl in their arsenal - it's just called mae ukemi (it helps if the emphasis is to drop down to the ground quickly, rather then a jump up in the air). Good grapplers still get taken down, though, so don't forget that you have ushiro ukemi to allow yourself to fall into the best position to get ready to get back to your feet.