Can VirtualBox be executed under Amazon EC2 instance?

No, I don't believe it will.

I'm not 100% clear on exactly why, but my understanding is that the VirtualBox host needs access to ring 0, but since your host will be running in a virtualized system it won't be able to get this access.

If you really want to run virtual machines inside other virtual machines, you can use QEMU. Because it is an a processor emulator it doesn't depend on any of the underlying hardware, so it will work “anywhere”. The downside, though, is that it's much slower.

Well, Amazon now allows to import VirtualBox and VMWare VMs. Not all operation systems are supported yet, but they work on it:

http://aws.amazon.com/ec2/vmimport/

So there is no need to run VirtualBox under Amazon, one can just import and clone the VM as an instance.