Like tourist, I regularly ride a sprung flyer (a b17 with springs) on my commuter, and I'd have to agree with tourists assessment. If I whack into a pothole it absorbs a certain amount, but because I'm a lightweight, I'd say the overall effect is limited.
I think it is more flexible or springy than when I got it years back, but just be aware that the springs are indeed pretty stiff.
you'd really have to do a back to back trial with your existing seat to get a proper idea.
I bought mine used just because it looks cool as an object with the springs and copper rivets, but I suspect for you and your specific serious back issue, a good suspension seatpost would be more effective.
if you were here I'd let you ride on mine, but to buy one, go through the leather break in period, only to find it doesn't help, would be a drag.
But maybe it would help, how much do you weigh?
oh, I'd seriously look at wider tires, the effect of a nice tire with volume and proper psi makes a huge difference in ride comfort. I've ridden a lot on 2inch tires that have fantastic suspension at the right pressures for my weight
what type of bike do you use? What's the widest tire it can take?