Don't tell them yes or tell them no. Test, monitor, and promote the path that leads to the best success rates, acknowledging that user growth may drive success in the longer term. Take the long view, basically.
Individual sites can't measure how much their combined spam costs them due to the ever more aggressive use of ad blockers. In the short term, a newsletter popup probably does increase revenue, but acquiring new users in the future will be more expensive as a result because the cheap and simple ads will fail to reach most of the market. Unfortunately, nobody has incentive to stop, as they'll just give up the short-term revenue and still suffer the future consquences from all of the other bad actors.
my wife has quit going to several sites altogether, and in other cases can not buy on a website, because of pop-up stuff.
So... if they're measuring for "email signups" then - w00t! - sweet! - numbers are so high! What about actual sales? Or repeat sales? Lifetime value of a customer?
I don't think I was very clear but yes, that's what I meant. You can't just look at the short-term gains of the promotion; if it suppresses repeat visits then that's a cost. And yes, it's hard to do, and is an art as much as a science.