That's not a recommended course of action. Email addresses fall under personal information in current legislation on user data, all which require a Privacy Policy for collecting personal information. You will open yourself up to liability if you request personal information without a Privacy Policy in place.
You'll need to have a Privacy Policy that explains that you collect email addresses, why you collect them, how you'll use them, and let users know about any rights they have when it comes to all of this. For example, let users know they can opt out of your email marketing list at any time, even after they've provided an email address and consent.