Sim, o VirtualBox pode executar um convidado de 64 bits em um SO host de 32 bits, com algumas condições, consulte os Perguntas frequentes sobre o Virtual Box , citadas abaixo:
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.