Is it advisable for wife with moderate to severe dementia to have full anesthesia neurosurgery to maybe relieve back pain?

We don't know anything about your wife's particular type of dementia, or any underlying medical conditions she may have.

We don't know what surgery is planned.

We don't know what her surgeon has identified as the cause of her back pain, or how severe the pain is, or what effect it is having on your wife's mobility and her quality of life.

We don't know the first thing about how the anaesthetists will handle her case.

And you're asking us?

If you have concerns, talk to her surgeon about it. What you want to know is whether the benefits of the surgery will outweigh the risks. You can also ask whether there are alternatives either to the surgery, or to general anaesthesia.

There are many reasons for back pain. It can sure make life awful.

I would try acupuncture, chiropractor, CBD oil, and even Massage before surgery.
Back pain is very common. I suffer from two types. CBD oil helped me tremendously with lower back pain. Chiro adjustments also help. Often I never get to the adjustment part as I am too tight to receive an adjustment. The equipment they use to loosen my muscles helps tremendously. Not sure what it’s called. Reminds me of a car wax buffer. It usually lasts for months for me.
I’ve never tried acupuncture but I would before surgery. I’ve had back spasms for about 20 years. Usually brought on by some repetitive chore. Veggie chopping etc. think Thanksgiving or Christmas gift wrapping. An area gets inflamed and the pain can be awful. Occasionally I would take a muscle relaxer and go to bed and try to “sleep” it off.
Only happened once or twice a year for about 15 years and then lower back pain like sciatica began. Had that chronically. I discovered CBD oil about two years ago and I can’t believe how much it has helped. Amazing.
I also use the disposal thermal wraps and sometimes Advil. It just depends on what I have on hand when the pain starts up. Walking everyday keeps it away for me but if I get out of the habit it starts up when stressed.
So try some things first. Taking Advil is a last resort for me but that pain sure gets my attention.
Here is a great article from Harvard suggesting conservative treatment before surgery and good advice on the types of surgery. It’s not without risk aside from the anesthesia which can be significant as we know.

https://www.health.harvard.edu/pain/when-is-back-surgery-the-right-choice

There are no guarantees. All surgeries involve risks of all sorts. Will she be able to follow-through on her post-op PT? Or comply with any medications prescribed? Will you be able to provide all the post-op caregiving? I totally understand your concern about the anesthesia. Have you thoroughly researched less invasive options to relieve her pain? Since she already has dementia, I might be of the mind to risk the surgery but she would need to be in quite a bit of constant pain with no relief from other therapies to compel me to put her through it. Could you live with yourself if the worst-case scenario occurred? May you have peace with your decision and success in helping your wife become pain-free!