I don't see why not. We have been learning how to use Amazon Web Services, and I can say that creating a server in the cloud and installing ArcGIS Desktop is not very different from installing it on a physical computer. The way our IT has set us up, our AWS machines can join our Active Directory domains and reach our internal resources.
It sounds like your IT is already working on a plan, so they will have to deal with all the network connectivity issues to the databases and file resources you will use (and printers), but that will be something they are already aware of. You may have issues if you need to be able to plug in USB memory sticks, portable hard drives or CD/DVDs. If that is something your workflow requires, be sure to let your IT know that.
I do wonder from where you and your fellow GIS users will remote to these remote desktops. From a laptop or a desktop computer, I would guess.
GISP