No, we use them for some freestyle drills/exercises in my sword line. I know some ryu-ha use them to make kata/kumitachi a bit safer (meaning that as speeds increase, getting hit occasionally happens) but in our exercises there is the guarantee that you will be making contact since they aren't used within the context of a pre arranged form and we don't wear any bogu. The impacts are deterrent enough for me.
We use the shinai in various ways. First, we use them in taking the practice of our sword kata up a notch. The use of the shinai allows us to cross into an area in which the form is a bit more competitive in that if you miss your move, the partner will really hit you. We don't use any protective gear for this.
We also use the shinai as part of what I call "intention" training. For this we use gloves and helmets (we use a helmet originally designed by Grandmaster Canete of the Doces Pares Escrima style for full contact stick fighting. They are better padded than kendo helmets.) I took some basic exercises directly from the Maniwa Nen Ryu. Basically one person attacks full speed and power with continuous shomen attacks while the partner responds with any one of several responses. If your attack is better than the partner's response he gets hit. If the partner's shomen is better than your response, you get hit. It's not free sparring so there is better control of the form it takes but it does have the aspect that both partners are trying to strike the other. It's a tremendous exercise.
Sometimes we also put on the gear to test the individual moves within a form. if there is a tsuki attack, we put on the helmets, which have some neck protection, and try to really do that thrust attack. The partner will attempt to do whatever the response was in the form. You get to see if your tsuki attack is really capable of striking someone who isn't cooperating. People develop much greater speed by practicing this way.
Finally, we find that shinai are a valuable aid in developing solid irimi skills for weapons taking. With the bokken there is almost always a bit of energy held back since no one really wants to injure his partner. But with the shinai, your partner knows he won't injure you if he strikes you and is therefore more than happy to strike with full commitment. You find out pretty quickly if you can do an irimi or not.