Sure, that is possible.
The wiring (and the costs to put them in place) could be more expensive than the Arduinos.
With long wires, the Arduino must have more protection against electrical spikes. Perhaps even optocouplers.
If you have a working module, you can make 16 of them. That is not hard.
An Arduino Pro Mini clone costs about 5 dollars on Ebay.
Making the modules to talk with each other, increases the complexity a lot.
On the other hand, having a single unit, will make it a lot easier to take all light sensors into account.
There is not need for the modules to talk with each other, since you have all the information in one Arduino.
I'm still curious, what kind of proximity sensors ?