The best way to think about affiliate marketing is quality over quantity. There are a lot of small websites that will promote your product, but the key is finding a small number of partners that will deliver conversions. For example, an equity management services firm has over 20,000 affiliates in its system, but only about 25 affiliates generate 85 percent of revenue.
If you have pop-ups and optins on every page, I would have to think that it would be a lot harder to convince someone to link to it. Especially since the pages where you have your optins (and probably receive the most traffic) are probably the same pages that you have your best content on as well that you'd be hoping to pitch in your outreach campaign.