Q: Can I increase the amount of bandwidth used to replicate a virtual machine to Azure via Azure Site Recovery?
A: The number of threads used by replication to Azure can be increased to up to 32; however, by default Azure Site Recovery will try to use as much bandwidth as possible. To increase the number of threads used, create the registry key HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Windows Azure Backup\Replication, add a new DWORD value called UploadThreadsPerVM, and set a value up to 32. Data is sent to Azure blobs via REST APIs via Azure Site Recovery.
If you have a site-to-site VPN from on-premises to Microsoft Azure, then that site-to-site VPN won't be used; instead, data will be sent via the regular Internet connection. If you have ExpressRoute, then ExpressRoute will be used for the Azure Site Recovery traffic, as documented on Microsoft's Virtualization blog site, in "ExpressRoute + ASR = Efficient DR solution." This is because whereas a site-to-site VPN is from your infrastructure to your Azure Virtual Network only, ExpressRoute provides the connectivity to your Azure infrastructure, as well as the Azure public services such as storage interfaces.