In a form, if users had to check a checkbox to receive further marketing emails but couldn't continue the transaction unless they checked it, what do you think the drop out rate would be? Does anyone have any data on this? This kind of behaviour is effectively forcing opt-in to continue a transaction.
p.s. I completely disagree with this, but I want some data to back up my argument that it's not a good route to go.
Empirically, think of this as a wall. People hate walls. Here is Norman Nielsen's tiresome attempt to explain how bad walls are (in the case of an analogous world of log-in screen). https://www.nngroup.com/articles/login-walls/
But I do just want to take a moment ask, why do you have to get consent to send emails? What business are you in that marketing mails are deemed more valuable than a site transaction? That just seems crazy to me! A site needs to be all about conversion and removing roadblocks like the one you're mentioning. So...if they give you their email address, can't you just send them emails? You don't need a checkbox in addition to that. The email input field is the consent.
Unless you're doing this in a country where it is illegal to send email marketing to users or something, you could just send them email. Honestly, I expect that when I sign up for something that I will start being opted in to emails...and I could always opt out/unsubscribe if I want. The added checkbox that "forces" them to check it, is just silly at that point.