That is what many marketers do, yes. I've worked in ads, I know how it works. If the numbers aren't there, they usually don't continue.
In this case, however, a pop-up on your own site costs nothing. In fact, removing it incurs costs in development time, even if it's a simple line delete.
So, I am 100% sure no marketer would ever push for removing it, unless end-users specifically tell them that they are not going to use the site because of the pop-up. The likelihood that they realize that on their own is next to zero because of the difficulties in retention analysis to catch this.
Again, only my experience at past employers, but in a lot of cases the developers don't get heard when making these suggestions.