Yes, we need to have the 32 bit Java installed to use iTest. To install and run iTest on a 64 bit machine, we need to install the required 32 bit libraries. Follow the steps provided in the below Knowledge Base link to install these 32 bit Libraries.
I currently run iTest in a VirtualBox VM running 32-bit Ubuntu 12.04 LTS and it works great. If your machine is unsupported, I suggest you go that route. (I tried newer versions of Ubuntu, but ran into gtk problems.)