Most definitely. They go hand in hand. Reading reinforces proper grammar and spelling and increases your vocabulary, which in turn makes you a better writer. Reading also exposes you to different styles of writing, which helps create your own style and makes your writing interesting to others. This is one of the reasons it is so important to get children to start reading at an early age.
You don't have to read the classics...just read about what things that interest you. For instance, I'm not a big poetry fan, most of it goes over my head. I like biographies and history books. Some people like to read technical books - but it all has the same influence. The more you read the better writer you will become.
If you have children that need to be encouraged to read, you may want to check out my Hub "Top 10 Ways to Encourage Children to Read." You can find it at: