My mom currently has moderate Alzheimer’s. She wears depends 24/7 for urinary incontinence and now has fecal incontinence.

My late husband when his urinary incontinence was off the charts was given Botox into his bladder by his urologist in his office to try and help calm his bladder down so he wasn't peeing so often.
He did NOT have to go under any "local anesthesia" when he had that done. Plus it didn't help him at all.
I highly doubt that anything will help any more with your mom having Alzheimer's as incontinence seems to come with any of the dementias.
I wouldn't continue to put her through these stressful situations/treatments any more, but instead just let her be as comfortable as possible and just make sure she's being changed on a regular basis.
Most doctors anymore only care about their financial gain and not what is best for their patients. Sad but true.

well, she now has the double incontinence. Assuming she is ok with wearing depends and getting regular changes, it might be best to leave it be with that. I would assume there are possible downsides to the botox and also the anesthesia. Risks of procedures and anesthesia do increase overall with age. I have no idea about your exact question about benefits, except to say that if she is ok with regular depends use and changes, thats a good thing! Be glad she is allowing the wearing of Depends! Some refuse them!

Is Mom asking to go to the bathroom all the time ?

Let her be if she isn’t complaining about frequency or urgency.
She is already incontinent , that most likely won’t change.

If it were my mother I wouldn’t bother at all , I doubt at this late stage it would do anything .

Your mom had Botox in prior years for urinary urgency issues, not incontinence. Plus, Botox is not going to address fecal incontinence anyway, so what's the point? The vast majority of dementia sufferers are incontinent no matter what meds are taken, and once the later stages of disease set in, it's inevitable. I'd leave her alone if this were my mom.