is the ps2 connected mouse's microcontroller programmable ?

The PS-2 connector has been around for a very long time. The small round one that is the standard today actually used to be a larger plug. I believe it was IBM that wnet to the smaller size. I have a box full of adapters to change from the one size to the other. Anyway, PS-2 used to be used for a lot of things besides keyboards. It is a powered plug so before there was USB the PS-2 port was often used as a power source. All of the early bar code readers used PS-2 and so did many of the early graphics tablets. So it could be used for more than just keyboard and mouse input. Mice used to be hooked up to a serial port and there would only be one keyboard port. The parallel printer port was often used for external drives such as a zip drive because it was the only port that could handle the bidirectional data transfer.
Now they are trying to phase out the PS-2 altogether. At least some MB manufactures are. And serial and parallel are long gone all in favor of the USB.
So while the controller in the mouse is not changeable the port itself can be used for other things. But in order to use it you would need to get the exact pin specs and be able to program whatever it is you would want to add in. BY the way, originally the keyboard port was controlled by a separate chip on the motherboard. There were times when that chip would go bad but the board would continue to work fine. When that happened then you had to get an add on card to get around it so you could keep using the system.

Its usually a mask programmed microcontroller, so you can't change it.

Steve