In theory, yes (you're going to need a bunch of glue code, though).
Not to deter you from using an Arduino, but using one technically complicates matters; there are tons of USB interface boards out there to allow digital i/o control, relay control, analog i/o, etc - all via simple USB interfaces (in many cases done with FTDI USB serial, like the Arduino).
Now - if your goal is to replicate one of those boards, and to use the Arduino in the development (ie, creating an embedded controller with a command set to control various relays and such - based on an ATMega uC); that is one thing. But if your end goal is just control of lights and such, other solutions are readily available, and save you that much extra effort (believe me, writing the controlling code and interfacing to all of the external lights and such will be tough enough).
Just a thought...good luck.
