Is there a way to attach the same disk to multiple Azure VMs
Azure Files is a feature introduced in 2014, that allows mounting the same VHD in multiple VMs over SMB 2.1.
Unfortunately I have no experience with it.
No you cannot not do this I believe. If you need to have shared storage best bet is Blob storage.
You could though create a share on from one of your VM's and allow access that way. But this has headaches with security and setup.
I would use blob storage.
The underlying Hyper-V can do this. It's introduced in Server 2012 R2 and called Shared VHDX. I was told Azure Web sites is using this mechanism. Unfortunatly it's not (yet?) available for virtual machines. The only option I think of now is that you setup file sharing (SMB) and have your VMs in the same virtual network so that they can access this file share.