That depends on whether your core project exports JodaTime in the order and export settings.
There are tradeoffs to exporting a third-party library. If your core project will only be used as part of your other projects, exporting the library makes it easy to ensure that all your other projects are using the same version. But if your core project is itself a library that you're going to publish, you usually don't want to export third-party libraries because then they effectively become part of your API. In fact, you may actually want to design your API to conceal what third-party libraries you're using in case you ever want to switch to something else.