Yes you can, not crazy at all, in fact that is what the ODB data port is for. At the device level you can read info just using a terminal window on your PC, (will help you develop the arduino code) or most people like to use a software app to read codes, clear, read the PIDs (parameter ID's) and most of the O2 sensor data is in mode $05, most software has a good interface for this. The cable should come with some freeware OBD apps, but none will allow reflashing through the cable. That is a whole other animal, and differs depending on if pre 2008 or 2008 and later. 08 and later we can only read PID's by id and possibly by address, but no modes are really supported on the 08 and up stuff from my observation. I also use one of the small canned OBD gauges that is a bit more self contained for a heads up display in the car.
To write code for the arduino, there are several libraries currently for OBD messaging, and many of the PID message strings are setup in the libraries. Stanley the guy that runs freematics OBD stuff has written a ton of code for OBD data logging and has shields and LCD displays that are all arduino friendly. Some stuff is turn key, others you can just get the idea how to log data, and whatever your imagination brings. Fun stuff. I have one of Stanley's freematics OBD shields for a mega and it is pretty handy for logging sensor data and even deriving the fuel and ignition tables with a little math coding.