Sorry if I was not clear enough. In any case with Campaign, you'll use automatically Adobe Mobile SDK. You will configure your mobile application in both Campaign and Adobe Mobile Services (both applications will work together). Then, from Campaign, you'll be able to send your push notifications, and to retrieve profile data collected from the application.
If you plan on sending push notifications as part of your campaigns then yes Adobe Campaign is the right product (Also, seing your use case, I assume Campaign would be good for that). Adobe Campaign push notification service works with Adobe's mobile SDK as well. I'd recommend you to go through the following links from the Adobe Campaign documentation: Push configuration and About push notifications. You may find the info you need.
Let me know if you'd like more specific information.