Wouldn't it be possible to run a clone while it is still being cloned?
AFAIK a clone is created, by first snapshooting the source. Then the snapshot is copied as the clone, while the source VM continues to run. All changes made to harddisks are stored in a delta file, which is incorporated to the snapshot after the copying is complete.
Why couldn't that be done to the clone in the same way?
It is started as a snapshot with a delta file. The reference would be the snapshot of the source VM, until that is completely copied. After that, the delta files is incorporated to the clone in the same way as for the source. So while copying, you have one unchanging snapshot for both source and clone and two delta files, one for each.
With this mechanism you could create clones on the fly and use them instantly. Would be a quite nice technique for desktop virtualization: every new connection creates its own clone. At logout, changes to the Windows profile are copied back to the profile server and after that, the VM is simply destroyed.