Google's John Mueller added some clarity around how Google processes links within a disavow file. He said on Twitter that the disavow file is "processed immediately and taken into account as the URLs are recrawled."
Here is the tweet:
It's processed immediately and taken into account as the URLs are recrawled.
— 🍌 John 🍌 (@JohnMu) February 17, 2020
Previously, last year, John Mueller said something similar he said Google will process your disavow link file immediately, it will take some time for Google to disavow the links within it. Here is that tweet:
The files are processed immediately. The links are disavowed over time - there is no fixed timeline.
— 🍌 John 🍌 (@JohnMu) June 1, 2019
What does this mean? Well, John is saying the same thing. You can disavow a link today but Google won't process that disavowed link fully until the URL is recrawled. And of course, it can take a while for Google to recrawl all those URLs. So maybe, if you can, you should push Google to recrawl URLs you have access to but if you had access to them, I guess you wouldn't need the disavow tool?
Forum discussion at Twitter.