Sorry, I can't offer any blanket guarantees. Yes, if it's a working VirtualBox VM then CloneVDI should be able to clone the drives. With compaction enabled this may go faster than you think. CloneVDI does not clone VMs, you'd have to create the VM yourself.
If it was me then I'd set up the new server separately, get it all ready to run so that all you have to do is swap over the cables. I assume the server has some kind of internal backup mechanism that can take care of bringing it right up to date relative to the few-hours-old version which was cloned.