We have a box with a Texas Instruments ARM Cortex A8 as the processor running Linux and KDE. Is it possible to use KDevelop on a Linux PC to develop applications for the TI based box? Has anyone ever used KDevelop for cross application development?

Yes, I have written code using KDevelop for an ARM Cortex M0 -- which is a bit smaller of course

Seriously though, KDevelop doesn't care, it doesn't do anything with your build environment. I used CMake for compiling my code for the Cortex M0, which worked just fine, and it's no problem to use it with KDevelop. You can also write custom makefiles and use the custom makefile project manager.

Greetings,
Sven