The only things that matter when you add hard drives are:-
1). Capacity and whether the hard drive controller can handle it (drives larger than 2TB need special controllers)
2). The physical interface between the hard drive controller and the hard drive e.g. PATA, SAS, SATA
3). Space within your case to mount the hard drive
The architecture of the operating system does not matter as the hard drive is still formatted with a standard file system that both architectures can read and write to. The only caveat to that would be that you cannot install 64-bit programs onto a 32-bit operating system.