Yes a sleep number bed that is adjustable for your comfort can help when you have back pain.
With a traditional mattress you can't adjust the settings for the comfort of the mattress so you're stuck with how comfortable or uncomfortable the mattress is.
But with a sleep number adjustable mattress or bed you can dial in the settings to adjust the comfort of the sleep number bed to help alleviate the back pain.
I have a sleep number bed and I love that I can adjust it depending on how my back is feeling and I sleep much better on the sleep number bed than I did on my regular mattress.
The sleep number bed and mattress are well worth the money spent on it and it should last a good 10 to 20 years before you need to or want to replace it.
The Purple Mattress is also another good comfortable mattress for people with back pain as well as the Tempurpedic mattress.
I would recommend going to a mattress store and trying out some mattresses to see how they feel to you and your back.