I think if the links are broken and Google has been made aware of such, ie it has recrawled and cached the page (simply add "cache:" in front of the URL for the last cache copy - if the URL itself is broken, check if it is still indexed in Google), then it would know that the link has been broken and shouldn't count it.
If that's the case, I don't think the disavow would have any benefit, unless of course if the link were to return, which could be a possibility.
If the page is cached and that cached version has got the broken version = no worries.
If the URL is broken and the page is no longer indexed = no worries.
If the URL is broken and still indexed = check to see if any other links point to that URL (including the URLs site navigation and/or sitemap, if applicable. If not, should deindex soon. If there are links, I'd disavow.
Just my two pennies, hope it helps!