Yes, resting IS important for your Disney vacation to be enjoyable. It should be part of your daily plans.
Along with all this walking I walk to emphasize the importance of rest, which can be completed in several ways. These ways include, but are not limited to: sitting down dining in table service/quick service restaurant (I prefer table service), using a sit-down ride/attraction that is inside (or partially indoors) ride with A/C and comfy seats that last for more than 20 minutes, or just finding a seat on a bench that is off the main path with a cool bottle/cup of water. Believe me, there are options for this in every park. If you are there with young children and/or infants you are nursing, please check out the baby care centers in each of the parks. You will be glad you did. Check this out on your paper maps or on your My Disney Experience App.
I cannot over stress the importance of rest. It will save you for melt downs and discontent among your travel group (this goes back to know the group you are traveling with). Remember, we want this to be fun!!
For those avid runners, joggers or walkers Disney also has trails at each resort for you to use. Here is the link: https://disneyworld.disney.go.com/recreation/jogging/ Happy Trails to you!!