You should be able to install and go, as long as you have the Desktop Client on your computer and can connect to the BES to regenerate an encryption key.
You can't use every feature of 4.0 on the handset until your admins upgrade the BES to 4.0, though.
I can't install OS4.0 (or any other app) on my work computer.
I installed desktop and 4.0 on another computer and was planning use that to install 4.0 on the BB. Could I then regenerate the key on my work computer? Does it matter which version of Desktop I use to regenerate the key? I believe we have Desktop 3.5 at the moment.