To achieve what you want, you need to create a template image with your custom application in it and then use that image to create an Azure RemoteApp collection.
To create a template image with your custom application, you can follow these steps: https://azure.microsoft.com/en-us/documentation/articles/remoteapp-image-on-azurevm/ (basically, create Azure VM, install your app on the VM, sysprep, save the image to Azure RemoteApp)
Then, your image will appear in the list of images when creating a collection and you can follow the steps here to create a cloud collection: https://azure.microsoft.com/en-us/documentation/articles/remoteapp-create-cloud-deployment/ (pick the aforementioned image)
We have more documentation about the service here: http://azure.microsoft.com/en-us/documentation/services/remoteapp/ and we have other means of support here: https://www.remoteapp.windowsazure.com/en/support.aspx
/cd
P.S.: I work on Azure RemoteApp