If you have a landing page, and on that landing page there is a tooltip that "pops up" when the user rolls over an image -- is that a problem? I would venture to say that no PPC/SEO expert would say that it is. That is what we have -- it is like a tooltip that allows the user to enter information.
The more obtrusive popups compel behavior. Our implementation does not. After seeing our popup, the user can still use the back button, close the browser, navigate to another URL in the address bar.
Our thinking is as follows: we have a special purpose web site that is of no value to anyone other than those who need our service, which is not everyone. We pay to get visitors to our web site. If they came to the site with this need, then we would like both a "second chance" and also give them the opportunity to check some boxes as to why they are leaving. This will help us to better meet their needs and reduce the number of visitors in the future who do not come to our site with this need.
In other words, it helps us to do better in reducing the number of "misfires" which helps everyone in the long run.
We have been evolving our web site for over 8 years now, and it is "optimized and focused and clear" as we have been able to make it -- SO FAR. But we agree that we can do better, and this will help us to do so. I am only making this point to counter the potentially valid argument that our site is badly optimized. I can assure you that every word on the site gets reviewed and is there for a purpose.
We agree that continual effort to "optimize better" is a important goal and we pursue it vigorously on an ongoing basis, but improvements in SERP placement will only have minor impact at this time, because already we are consistently in the top 3 in the organic and frequently #1.
In any case, we feel that if the user is on our landing page in a "complete miss" then there is no harm in presenting a popup that does not compel behavior but only requests their input, which they can chose to ignore. But if they have come to our site and could use our service, then they deserve the "second chance" to see that, and we deserve the ability to make our site better by providing the "survey" aspect.
Having said all of the above, we do not take lightly adding this function, and thus I am seeking through various channels viewpoints of experts. So I am not trying to be argumentative, but to make the best case possible. If this case still gets shot down, then so be it.
Again, I think the best way to look at this is on a spectrum with many points. For example, a page with pure content and no links or interactive opportunity at all would be the "innocent" end of the spectrum. A page with window.open popups and pop-unders and you can't get out of it and it goes on indefinitely -- that would be the other "guilty" extreme. A non-interactive page with tooltips such as alt or title tags would be closer to the innocent end. And our proposal with tooltip-like popups that do not impede the user but give them opportunity to enter data would be just a bit further.
My position is that our approach is still "innocent" and should not violate G's rules.