Can an optical mouse sensor chip (System On Chip) which has a digital signal processor, Serial I/O, and a set of registers be considered as a Micro-controller?

Microcontroller by definition should be capable of controlling a system the way it is flashed with a code.  For that to happen you need a programmable memory and an instruction set which can be used to program. I would consider optical mouse as a sensor device. Some sensors do have registor which carry configuration bits, e.g a optical mouse can have registors to control speed, acceleration of pointer, right/left handed mouse,etc. These make it configurable sensors and will not qualify it to be a micro-controller. Regards Niraj