In my case, I've done three batches of disavows. Roughly speaking it takes about 10 days for this to kick in IMO. I got slight upward bumps after those time periods. I can't say that definitively though because google is constantly changing so correlation might not be causation.
But overall I have not returned to my previous ranking and have done a LOT of work manually removing links and accurately disavowing the ones I can't scrub.
If there is a success story for link scrubbing and algo penalties (NOT manual penalties...those are relatively easy in comparison), then I would love to see it.