Even though there are thousands of domain names involved, I wouldn't expect for this to have any positive effect on your site's SEO (or rankings). The problem is that these domain names aren't trusted--they aren't going to have any Domain Authority, they're hosted most likely on the same server (or class C block of IPs), and the content isn't unique to each site. For SEO and ranking purposes, unfortunately you have all of those things counting against you.
In order for a site or a domain to help, it needs unique content, higher Domain Authority, and links to it.
This shouldn't stop you from using those domains to your benefit, though. I would, however, either put up an ad that contains a link, or put a text link on the pages. I would also make sure those are "nofollow" links. Suddenly if you have 20,000 sitewide links to your site from "low quality", thin content domains, that could actually throw up a red flag and hurt your site's current rankings.