Yes.
Anyone with an Apple ID can use Xcode and build an app. They can even install it on iPhones connected to their Mac. What they can not do is access the parts of the Apple Developer website that control certificates, identifiers, and profiles. Those are required to work with push notifications. A paid Apple Developer Membership is necessary to use push notifications.
A free developer account can still work with notifications using local notifications. Local notifications can be a great tool for prototyping push notifications. In many cases, local notifications are a better choice than push notifications.