The United States ratified the Nuclear Non-Proliferation Treaty (NPT) in 1969 after the U.S. Senate advised ratification in accordance with the U.S. Constitution, and the treaty went into effect in 1970. Can the administration issue by itself an order that conflicts with that treaty?
This question has not been raised, much less answered. The Iran Deal, formally known as the Joint Comprehensive Plan of Action and signed by the administration, conflicts repeatedly with U.S. obligations as a signatory of the NPT.
The issue is not whether the executive can without a treaty enter into agreements with foreign governments. Of course it can. That happens often from negotiating minor details of landing rights to major agreements. But these executive agreements are done consistent with treaty obligations, or certainly not in conflict with them. The Iran Deal conflicts with the NPT.