I am wondering if I can connect an Arduino to my computer via the 5V, GND, TX, and RX pins. I read that the USB data lines on the connector aren't connected to the TX and RX pins, but does it work in reverse?
You didn't specify which of the many Arduino boards of which you are speaking, but most have a 2nd chip on them for interfacing with the computer via USB.
Testing with a USB cable of an old wired keyboard, which has IDC connectors, the Arduino only comes on, not recognized by the IDE. I read this saying that it is slower, and now that I think about it, there is no use for this.