Q. Can I convert a General purpose storage account to a Blob storage account in Azure?
A. No. You cannot convert accounts between storage account types (also remember the Blob storage accounts only support block blobs and append blobs therefore other types of storage service could not be migrated anyway). If you wish to convert you would need to create a new storage account and perform an Azure-side asynchronous storage copy operation to move the data between accounts. I have an example script to copy content between accounts at http://windowsitpro.com/azure/copy-content-one-azure-storage-account-another and http://windowsitpro.com/azure/retrieve-storage-context-arm for how to get ARM storage account contexts.