Yes, having full support while sleeping can help with back problems.
I have a fully adjustable bed and it makes a difference. Just play around with it to find what works. I like to have the head and upper back area slightly raised and the feet too.
My lower back is a wreck from lifting heavy.
It also helps my bad knee, for some reason having my feet slightly elevated helps prevent knee pain.
Also having a semi-firm mattress without slumps in it can help your spine. The old cheap mattresses do not support very well.