SharePoint 2013 and SQL Server can be installed in Azure VMs - however, does such setup support Remote Blob Storage (RBS), namely FILESTREAM RBS? I know that SharePoint Online doesn't support RBS, how about SharePoint with Azure? Note that I don't mean Azure Blob Storage, which is something else.
I don't see why not. I havn't tried myself, but as long as you put your VMs and storage accounts in same affinity group, I would assume that Azure's internal disks are fast enough to be wihtin the 20ms latency requirement, but a test would be the only way to know for sure. Also be sure to look into striping your disks if you want to obtain good IOPS. Read more here: http://msmvps.com/blogs/nunogodinho/archive/2013/04/22/lessons-learned-taking-the-best-out-of-windows-azure-virtual-machines.aspx