Can I install our proprietary software inside the camera and resell it as our product without providing the source code for our additions?
Usually yes, but that depends. As with any software running on GNU/Linux system you may install (and distribute) proprietary software without disclosing the source code if it is not compiled with or statically linked to the software cover by the GNU GPL. Basically these are the same rules as with the computer running software covered with this license. What is legal on the computer is legal in the camera, what is not – is not. All the Elphel software installed in the camera including drivers that provide processor interaction with the FPGA and the image sensors is covered by GNU GPL.