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.)
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.