Keep in mind that everyone's body is different, and issues are different, so it is difficult to say YES it will solve your problem.

The mattress you are asking about is built on a Bonnell coil system, which means that your support comes from the foam above the coils, as a Bonnell coil is a wire-tied coil system: all the coils are connected and unable to conform to the curves of your back. And once the foam loses its support, there goes its ability to conform and support.

A better surface for a bad back is one that easily gives and fills in, such as a solid foam bed or a pocketed coil bed. Both are able to fill in the lumbar and give gently in the hips and shoulders.

The Seagrove uses an interlocking coil system that provides rigid support. To say if this is good for you, is unknown based the information you provided. Beds as rigid as this one works for severely damaged spines...mostly discs that are herniated and bulging discs that are about to herniate. That being said, it works for males with these problem more so than for females who are curvy...too curvy for such rigid support. The Seagrove firm is an excellent value if the price is right. You may find that sleeping on a mattress this firm is uncomfortable...as to not allow you to sleep deeply. You can add a couple of inches of soft Talalay latex, which will provide you a much more comfortable, deep night's sleep, without sacrificing the underlying firm support

Let me address back pain. If your pain is higher in the morning than at night, it may be the bed you are sleeping on. There may also be some health issues, so don't ignore that. To receive relief from back pain, it is important to find a bed that puts you in a good posture position. Take your partner or a friend with you and lay on this mattress. Have your other half look closely at your body's position while in the bed. Does it look like it would if you are standing upright? If it does, it is offering good posture. If not, it will stress joints in the shoulders, hips, and spine, causing them not to regenerate fully at night.

For someone with back pain, most spring mattresses will not offer much help. The very high end might. Consider other technologies like air or foam (preferably latex) that will allow your body to feel less pressure. The major air company says well over 80% experience pain relief on their beds. The major foam player has similar statistics. There are alternatives that will allow you to sleep better, and at a better value.