I tried to set up a similar (identical) scheme for use internally, but for some bonkers reason Microsoft's CA on 2008 R2 makes doing this almost "impossible." Or at least if it is possible it is insanely complex. It just really hated and rejected the concept of an offline root CA that didn't have a Microsoft CA running for it.
I'd love to be able to tell everyone doing an internal/corporate key-chain that "this is how it should be done" but holy heck does the tooling make it more complicated than it needs to be. I should just be able to install the public root key, hide the private root key indefinitely and it should "just work" for any key generated via the two intermediate CAs.