Potential problems you will face are that the amount of current required to drive the LED may be more than what the MAP sensor wants to put out, or the current drive could be enough to affect the reading. Also, you would need to match a current limiting resistor to the drive capability of the MAP sensor so that you don't get too much current through the LED at max MAP output, but still have enough at the lowest MAP value where you want it lit.
Do you have access to constant voltage from elsewhere? Even the 5V supply to the MAP sensor(assuming it has one) would help you out. If all you want is for the LED to come on with the switch, and you have a 5V supply, and 4.3V LED, it would be pretty easy.