I have not tried Helicon Rewrite on Azure yet, but i don't see any reason, why it should not work on Azure. A webrole has a fully manageable IIS, where Helicon Isapi Rewrite is not installed per default whereas IIS URL Rewrite 2.0 is!
You can either install and configure it via Remote Connection or via "Startup Tasks".
My suggestion to you: Try first to get Helicon Isapi Rewrite running via RDP. When you see its working, try to automate it with "Start Up" Tasks. This is recommended because changes on Webroles with RDP are non-persistant.
Further Reading:
Startup Tasks: http://msdn.microsoft.com/en-us/library/windowsazure/gg456327.aspx
Manual Installation: http://www.isapirewrite.com/docs/#install