Do clownfish live in the intertidal zone?

Yes, some reefs are exposed at low tide, especially extreme low tide. This puts a strain on coral, and some experience periodic bleaching in the warm water/sunlight.

Source: experience with the reefs in my home town of Darwin in northern Australia which experiences extreme tides. During the low spring tide it is possible to walk out on top of the reef and look at the exposed colourful coral, anemones, sponges and other reef life. I am sure that there is only a rather limited subset of species which can survive in this zone as opposed to permanently underwater.