It sounds like you want a bunch of separate systems/circuits running in the model (lights, sounds, etc...) and have the Arduino "switch" them on/off at random intervals.
Yes, this is extremely possible.
Depending on certain variables you can use FETS, relays, analog switches....a number of components to turn them on/off.
For code, it could akin to any example you find that turns on & off an LED. Incorporate the 'random' function and the premise behind the "blink without delay" example.
If you're building the display cabinet, you'll want to include a false back, or space in the base, to hide the arduino and necessary support circuitry.
As you have more specifics of the project, we can give you more specific advice/direction on how to go about it.