No you can't. The trait is a feature of the class, and php yanks it in there, has to resolve conflicts (or find out they aren't resolved) at one time, so you define it at the class, and that's it.
You really do have to ask yourself if you want to use them like this though. If a class might or might not have a trait, is it really a class? and are you using the trait correctly? Hard to say without your usecase specifically, but I dare to guess this is almost always a code-smell.
If you are using traits in a good way, you can probably just use them for the whole class?