From the Virtualbox 2.1.2 User Guide, section 1.6:
64-bit guests
Starting with Version 2.0, VirtualBox also supports 64-bit guest operating systems.
Starting with Version 2.1, you can even run 64-bit guests on a 32-bit host operating system, so long as you have sufficient hardware.
In detail, 64-bit guests are supported under the following conditions:
You need a 64-bit processor with hardware virtualization support (see chapter
1.2, Software vs. hardware virtualization (VT-x and AMD-V), page 10).
You must enable hardware virtualization for the particular VM for which you
want 64-bit support; software virtualization is not supported for 64-bit VMs.
Note: On most systems, the hardware virtualization features first need to be
enabled in the BIOS before VirtualBox can use them.
If you want to use 64-bit guest support on a 32-bit host operating system, you
must also select a 64-bit operating system for the particular VM. Since supporting
64 bits on 32-bit hosts incurs additional overhead, VirtualBox only enables this
support upon explicit request.
On 64-bit hosts, 64-bit guest support is always enabled, so you can simply install a 64-bit operating system in the guest.
Still seems like a dumb idea.