Can I use an external power supply and still communicate with my computer over Serial?
Yes you can. It still leaves the data/ground lines intact, it just doesn't bridge the 5V line.

Arduino Uno Schematic v.3:



The USBVCC is directly from the 5V on the USB jack (well, technically there's a fuse there). It then goes through a transistor (T1) that only allows power through when there is no power coming from the 5V regulator (that regulates the VIN voltage).

The USB jack:



You can see pin 1 of the USB jack (5V) goes through the fuse to USBVCC. The next ones D+/D- are the data lines that go through resistors to the ATMEGA16U (used for USB to UART). The last one just ties into ground.