My Raspberryπ has a serial console in its GPIOs. My logic level UART converter has four pins: GND, RXD, TXD and 3V3. It works without connecting 3V3.
Why should I want to connect the 3V3 pin to the Raspberryπ?
It's possible that the device is powered through the clamping diodes on the TxD input, since that will be higher than Vcc if you haven't that connected.
Doing so is very naughty, the diodes are meant as overvoltage protection, not for powering the device. It's not because something works that it's wise to use it that way.
edit re your comment
You hadn't said anything about the USB connection! In that case the 3.3 V is not unconnected: it's the output of an on-board LDO voltage regulator, which also powers the UART converter. Chances are that it's an FTDI converter, probably an FT232R. In that case the 3.3 V regulator is on the FT232R IC.
Up to 50mA can be drawn from this pin to power external logic if required. (p. 8)
Which is OK for a small microcontroller circuit, but not for the Rpi, which needs up to 700 mA.
You should not connect it. That 3V3 output can no supply enough current to power a RaPi. It is used when for instance a low-current 3V3 microcontroller is connected to the usb-serial converter.