Using Arduino Flora as a general purpose ID badge
Yes, you can find wifi modules with a serial interface that would work.

However, by the time you add the wifi module, you've increased the size to the point where you might as well use a regular arduino.

With a regular arduino you can add a wifi shield pretty easily.

As for your RFID idea, the easiest way would be to find an active tag that has an LED on it that blinks when it's transmitting, and then run a connection from that output to the microcontroller (would require some soldering).