Didn't know Java 6 was Intel-only -- sorry!
And yeah, all processors in Macs (whether it be a laptop or a desktop) are 64-bit with the exception of the Core Duo model Macs, which are limited to the very first MacBook and MacBook Pros (I believe).
It seems that all laptops released on or after October 2006 have Core 2 Duo processors, and, therefore, are 64-bit.
It seems that all desktops (with the exception of the Mac Pros and the XServe machines) released on or after September 2006 have Core 2 Duo processors, and, therefore, are 64-bit.