The Short Answer
No, you don’t need to sweat to have a good workout. It can serve as one indicator of how intense your workout was, but there are better indicators including heart rate or perceived exertion (how hard it feels). In other words, if you bust your butt, it was probably a good workout, even if you’re dry as a bone afterwards.
Conversely, just because you’re sweating buckets doesn’t mean you had a great workout. It might just mean you were really hot. Again, it’s better to go by how hard you worked, not how wet your shirt is.