You are correct. See below for some additional information
If you are using the Adobe Experience Platform SDK and you want to send push notifications to the app, there are a few options:
1) You can license Adobe Campaign Classic (supports push notifications only) or Adobe Campaign Standard (support push notifications and in-app messaging).
2) If you have previously licensed the Mobile Marketing add-on for Adobe Analytics you may be able to use our upcoming Mobile Services extension to send push notifications to your app.
3) You could use a 3rd party vendor for push notification and work with the vendor to build an extension for the Adobe Experience Platform Mobile SDK to share data such as ECID and lifecycle metrics.