Can an entry door unit with sidelight be disassembled and reversed?
If the two units are indeed modular as you've described, then you can probably make this work. Some caveats:


The two units are obviously connected somehow. This is probably done with a combination of mechanical fasteners (screws, brackets) and sealant. You'll need to figure out how to separate them without damaging the other seals and joints, and then you'll need to reconnect them using metal plates, etc., along with sealant. 
There may have been a weatherseal/mounting flange around the outside of the assembly when it was installed. This would now be behind the stucco finish on the building, and you'd have to cut it away without damaging your stucco. 
When you reinstall you'll need to weatherproof without the benefit of the flanges. Strategically placed, high quality caulk could do the job, possibly backed by rope caulk or other filler. I doubt that you'll have room for spray foam insulation, but you could use that if you do. I'd use urethane caulk on the outside. It's extremely sticky and durable.
I'm not sure what the threshold situation will look like. That's an area of particular concern, since leaks can eventually damage the floor system framing as well as the finished floor. I'd have a plan before I begin. 


Now if you have the means to re-work the stucco, you can cut it back a few inches and work the project as if it was new construction. That would be ideal, but obviously much more expensive. 



Original answer:

Not really. It was constructed as a unit, and reversing it would require all the hardware mounting locations to be reversed as well as the frame members. It would be a massive operation and you'd probably lose both structural integrity and weather sealing in the process.