Digital IC that draws power from data pins
Yes, there are commercial chips that make use of this concept.  The best known are the 1-Wire IC's from Dallas Semiconductor/Maxim; many are various kinds of sensors.  "1-wire" is a bit of a misnomer, as two wires are of course needed including ground.

A typical chip is the DS18S20 digital thermometer:



Note even though the thermometer is packaged in a three-pin TO-92 package, only two pins are used, 1 (GND) and 2 (DQ-Data in/out).  Pin 3 is a NC (no connect).  So there is no V\$_{CC}\$ supply pin.

The make use of a concept called parasite (or parasitic) power.



Instead of the V\$_{CC}\$ pin, power is harvested off the data line which is normally kept high (either 3.3 or 5V) by a pullup resistor back at the host microcontroller.  This keeps the capacitor, typically 800 pF charged.

Incoming data is directly read off of the data line using either a buffer or inverter as shown in the diagram.  Outgoing data is sent back to the host by enabling the MOSFET across the data and return lines, which temporarily shorts them together (the current will be limited by the pull-up resistor).

When data is sent on the line in either direction, the line is temporarily brought low.  When this happens, the diode keeps the capacitor from being discharged, and the capacitor keeps the chip powered.

Another example of parasite power, this time not in an IC, but an RS-232 level shifter that doesn't need a charge pump:



RS-232 signal levels are -3 to -15v marking (idle), and +3v to +15v spacing (active).  (PC's typically use -5V and +5V since they fall within that range.)  Level shifters must be used to converter the RS-232 levels to the TTL signal levels used by the UART in a microcontroller, and also to reverse their polarity (for the UART, high is idle, and low is asserted, opposite of RS-232).

Going from the RS-232 TX output from the PC to the input of the UART is simple, use the  positive (asserted) voltage to ground the TTL RX lead via Q2, and ignore the negative voltage so the TTL RX lead will be pulled high by resistor R1 in the diagram.

Going the other way, a low level on TTL TX will result in V\$_{CC}\$ (typically 5V) placed on the PC RX lead.  But where to get a negative voltage without a negative supply?  Since the PC TX lead is normally negative, it is used to charge up the capacitor C1 through the diode, much like the 1-Wire circuit.  This voltage is then used to keep the PC RX lead negative when it is not being asserted.