What? How is this even possible? Even if one doesn't set internal deadlines, I can't imagine avoiding integration commitments with any number of third parties, whether they be strategic partners, clients/customers, api/feed integrators, etc.
While working with external parties who expect things done by a certain date prevents the 'no deadlines' policy from working (by definition), we have observed that typically work expands to fill the time allotted for it. This means that from an internal product development point of view, telling your team that your product should be ready by Q3 of next year will almost guarantee that the product will be done by Q3 or later (with copious amounts of scrambling as Q3 approaches). When you eliminate the deadline, workers (I would argue) are more likely to complete the task in the actual time it SHOULD take, instead of letting the job expand to fill the deadline. (You could argue that instead workers will be lazy and take longer than it should take, thus demonstrating that deadlines are necessary.)
You have the actual development time, and you have the artificial deadline. If the actual development time is longer than the deadline, then trying to meet the deadline will be stressful and quality to be sacrificed for speed. Alternatively if the deadline is longer than the actual time, then work will expand and the team will be less efficient. In both cases, working without a deadline should prove the better outcome.