No, the dream pod doesn't provide the well rested moodlet. However, as far as I can tell it has the fastest energy multiplier out of all the EP/SP beds (despite what the buy mode catalog suggests), so sims should fill up their energy fairly quickly when sleeping on it. (The Super Sleeper from the Store is much faster.) I often use the dream pod at university with sims who have 8am classes for that reason alone.
Instead of the well rested moodlet your sims will get positive or negative moodlets based on their dreams. Once you decide what they will dream about you can influence the dream by clicking on the dream pod and selecting one of 4 options. Two will help make the dream a positive one, and the other two will make the dream a negative one. I just spam the good options until the sleeping sim is having a happy dream and make sure the sim stays that way when he or she wakes up. The happy dream moodlet lasts 12 hrs, has a small positive boost on mood, and provides some sort of bonus like increased job performance, skill learning rate for a particular skill, academic performance boost, money, etc. The types of dreams you can choose depends on your sim's Advanced Technology skill level. I think a bad dream will provide a dream moodlet with a small negative effect on mood. I'm not sure about the other affects of bad dreams, I don't usually give my sims those.
As the sim gains Advanced Technology skill they'll be more likely to have a happy dream on their own, and to push them into having a happy dream will require less spamming of the 'influence dream' option. I often use the the dream about Advanced Technology to boost their learning rate for that skill since otherwise AT is awfully slow to raise unless you travel to Oasis Landing and do quests for Emit Relevart.
If you aren't going to take advantage of the dreams or need them to replenish their energy faster, then it's probably better to use another bed. Bed assignments don't work either on the dream pod. Whether or not the dream moodlet + the bonus from the dream makes up for the well rested moodlet and lack of bed assignment is a game play choice, I guess. In some games I use them a lot, in other games not so much.
The other reason you might want to use a dream pod is for sims with the Unstable trait. In my experience sims with the Unstable trait won't get episodes when sleeping in the dream pod (well, technically from waking up from a dream pod). I often use dream pods for Neat sims since there's no covers to make up in the morning.