Will Sun Java 6 Update 30 (32 bit version) work on Ubuntu 10.10 (64 bit version)?

I should use Sun instead of OpenJDK because the support people for the API I am interfacing to referred me to Sun. I should use the 32 bit Java 6 because Sun/Oracle's website says that it is to be used if you are using a Web Start application. (It appears that my Java code talks to an API that is offered by a Web Start application.)