A solid question, but I don't know how easy it will be to get raw numbers on this, or if they'll apply to your specific situation. It's important from an early stage to establish a way to split test new features like this so you can get realtime statistics for your own use case.
Keep in mind, the answer to this question is heavily influenced not only by the pop-up, but by the pop-ups context.
For example, when and why is the pop-up triggered?
- When trying to access advanced features only available to members?
- As soon as the page loads?
- After a certain scroll depth or a delayed time?
- When trying to close the page's tab or navigate away?
In summary, this question is more complex than "How does A correlate with B?" There are additional factors that require consideration. Also, given your specific industry, desired call to action, and overlay design, you may see very different results. Employing split testing will help you tweak and determine if your feature brings about the results you want.