Yes, it should support that. I'd suggest creating the containers on the VMs using SSH as we've limited cloud support to Amazon EC2 and Rackspace US and UK. If you set up SSH public key authentication between machines it's pretty easy then to install new containers via Fuse Management Console.
Per the FMC User Guide section on Creating a Root Container, "fmc will run a script that downloads the binary files required to install a Fuse container, installs the container in the user's home folder...".
My private cloud VM is Linux, but has no Internet access. Is there a work around, perhaps?
So basically the fabric runtime will execute a script on the remote host that uses curl to download a distribution via the FMC server, extracts it and runs it, supplying a URL that allows it to connect back to the FMC server. The fabric provisioning agent running in that container will connect back to the fabric registry and deploy the necessary bundles/features/FABs defined in whatever profiles you've assigned to that container on creation. So the main pre-requisites are a proper version of Java, curl and tar, also the user account that you use needs a home directory for the script to download and untar the distribution.