Custom trained model in Azure ML
No you cannot. I had a discussion with someone in their development/support team on the MSDN forums and currently they don't support 'drag and drop' type of functionality. However you CAN serialize the model output and then de-serialize them in Azure. 

Note that the answer in the image is a bit outdated and there is the 'Create R Script' module to replace the serialization-deserialization steps within Azure. However I believe you can still serialize outside Asure (in your Desktop version of R) and deserialize them in Azure.

Link to the conversation in Image:
https://social.msdn.microsoft.com/Forums/azure/en-US/5944c342-79ac-4ada-8006-8edf40f36ee1/r-script-as-a-trained-model?forum=MachineLearning