Yes you VirtualBox can run a 64 bit guest on a 32 bit host OS, with some conditions, see the Virtual Box FAQ, quoted below:
VirtualBox supports 64-bit guest operating systems, even on 32-bit
host operating systems,[11] provided that the following conditions are
met:
You need a 64-bit processor with hardware virtualization support
(see the section called “Hardware vs. software virtualization”).
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.
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.
