They are probably partially compatible. With Duplo for example, it's easy enough to stack Duplo on top of regular LEGO bricks, but not the other way around. For stacking regular bricks on top of Duplo, you need to have bricks of the proper multiple in each dimension -- they need to be full height and a multiple of 2 in the other dimensions. The Quatro bricks are compatible in the same way -- you can easily stack them on top of Duplo or regular bricks, but not the other way around; You probably also need to do a transition layer from Quatro to Duplo to regular bricks.

I've seen people use Duplo and Quatro for space-filling when they needed a large amount of structural brick somewhere that won't be seen in the final model. Think having a LEGO city setup that has an underground level.