Emulating 64 bit OS in a 32 bit host using VirtualBox

Yes.

According to their manual.

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.

On 64-bit hosts (which typically come with hardware virtualization support), 64-bit guest operating systems are always supported regardless of settings, so you can simply install a 64-bit operating system in the guest.

Warning

On any host, you should enable the I/O APIC for virtual machines that you intend to use in 64-bit mode. This is especially true for 64-bit Windows VMs. See the section called “"Advanced" tab”. In addition, for 64-bit Windows guests, you should make sure that the VM uses the Intel networking device, since there is no 64-bit driver support for the AMD PCNet card; see the section called “Virtual networking hardware”.

If you use the "Create VM" wizard of the VirtualBox graphical user interface (see the section called “Creating your first virtual machine”), VirtualBox will automatically use the correct settings for each selected 64-bit operating system type.