Hi Michael / Chris

In this case, unfortunately I have a harsh experience which makes me differ with Chris´s experience; I would definitely go forward with disavowing if you are really interested on making clear for Google that you do not value those links, even if they point to non-existing urls

A couple of years back we had a client (and still have it) with a huge hack that produced thousands of links pointing to pages of our client´s hacked domain. We even suspected of a “black hat” maneuver to make damage to our client´s SEO through this procedure.

We had a hell of a problem letting Google understand that those links where empty and pointed to a 404, even after we deleted all the content and the urls didn´t exist anymore... strange behavior still happened from time to time and until the appearance of disavow tool….unexpectedly Google re indexed those links, even that they pointed already for YEARS to nonexistent 404 urls

I would take the time and disavow if you are really interested on Google not indexing those links.

I hope you can profit from this experience.

Cheers to you both, form sunny southern Spain!