Is the image processor like a GPU in the sense that it includes a particular set of instructions that make them more effective for encoding images and movies? Could a powerful mobile processor like a Snapdragon 800 be as effective as one of these brand name image processors with the right software?
The image processors referred to belong to a class of chips called ASICs (Application Specific Integrated Circuits) - and a GPU is a common example of an ASIC. An ASIC includes additional instructions or routines implemented in hardware which make them orders of magnitude better at certain operations.
For example: The Fujitsu FR-V chip designs (which the Expeed is based on) contain a number of hardware optimisations for common multimedia operations such as JPEG encoding and H.264 video.
For the same clock speed, thermal and power envelopes a dedicated ASIC will always outperform a general purpose processor at the task it was built to do, that's why you build them. Usually the ASIC is dedicated to its specialty task while another general purpose CPU like the snapdragon handles everything else and tells it what to do.
In summary, yes the image processor is like a GPU and no a mobile processor would not be as effective.
A dedicated image processor is uniquely designed, at the hardware level, to be extremely good at doing one specific set of known things. That differs from a general processor, like a CPU, which is designed to be as good as possible at doing an effectively unlimited number of unknown things. Without knowing exactly what kind of processing needs to be done, a general purpose central processing unit, such as the Snapdragon 800, could never be as fast as a dedicated image processor...all other things being equal (such as clock speed). The only way a general purpose CPU can be faster is if it has significantly higher clock speed and/or hardware parallelism...which at a certain point becomes to costly to be as effective as a dedicated processor. Hence the reason dedicated chips like EXPEED, DIGIC, etc. exist.
While the overall logic that a dedicated-purpose chip is always going to outperform a general-purpose CPU holds, the problem here is that the Snapdragon is not just a general-purpose CPU. It is a multi-core SoC that includes a dedicated GPU core (Adreno) with h.264 hardware encode/decode [mostly for video and games on the phone, but can be used for still images, too], as well as a DSP (digital signal processor) core (Hexagon) for RF processing, in addition to the main CPU core (Krait). So... whether it could smoke a DIGIC, with equivalent clock speed, data caches, and programming is really up for debate, especially since both have ARM-based processors.
OTOH, if you wanted to increase the wireless capabilities of a camera, all that extra RF processing hardware that phones and tablets use the Snapdragon for might come in handy. :D