No, you cannot send an email out through WordFly without an unsubscribe link.
You don't have to use the WordFly unsubscribe link, but you do need to have some way to people to unsubscribe. You cannot require subscribers to provide you with additional information to unsubscribe. It should be a one-click process. Make unsubscribing easy, transparent, and authentic.
If the WordFly unsubscribe link isn't present in your email, you'll see a red X when you are testing your email in the "Full Review" section.
In the event that WordFly is not recognizing your valid opt-out mechanism (e.g., your organization processes unsubscribe requests manually with a mailto link) WordFly will not prohibit you from sending the campaign. Proceed carefully.
WordFly will still let you send out your campaign, but you should think twice about what you're doing if you don't have an a valid unsubscribe link of some sort. Please review the WordFly Acceptable Use Policy for more information.
Learn more about unsubscribes in WordFly
Can I send an email without an unsubscribe link?