I'm not sure that a dethatcher would do anything to break up the clay, but I'm also wondering if you really need to do that. As long as there is sufficient moisture, the grass should be able to penetrate the clay. Some clay may not be great for growing grass, but some is (not all clay is equal).

If you use a spike aerator you will probably just compact the soil more and a core aerator will bring up dormant weed seed. As b7 notes, if you keep it moist you will have some grass.

With that said, so many people mistake their soil being "clay" because it gets hard as a rock. You would probably be surprised the make up if you did a physical test. Compact soil is normally a result of the lack of organic matter. If you want to soften it up google BL soil conditioner which is basically shampooing your lawn.