Short answer: Usually no.
Long answer: Sometimes, if the teacher wants the dog there (and even then, for a maximum of two hours). With adults and Service Dogs, (like a guide dog for the blind) the adult is in control of the Service Dog and makes all the decisions. With a child, though, it's still basically the adult i.e. parent, who is in charge, even though the Service Dog is for the child. An adult must be in charge because even the best-trained dog just doesn't have the cognitive ability to make decisions for the child. In other words, it’s usually too much responsibility to ask a child to control a dog and tell it what to do at school, thus, as a result, most schools ask that the child leave the Service Dog at home. So while some teachers and principals actually bring up the idea of a Service Dog and suggest that the parents get one for the child to bring to school, there are often other circumstances (such as limited resources) where having a dog in class makes a teacher's job harder, not easier. We believe that a Service Dog can be a great tool, and if the teacher wants the dog there every day, or even once in a while, that's great - but if the teacher doesn't want the dog there, that's okay, too. Of course, with the autism spectrum in particular, there are so many different symptoms and circumstances, so it really does depend on the situation.
Longest answer: For an even more detailed answer with examples, check out our page on Service Dogs in Schools.