Sensitivity on this is 185 mV/A with 21mV of noise. Page 5 of the datasheet. 20mA results in a rise of 3.7 mV. Since SF has enabled the noise filter, lets say this is reliably measurable (YMMV aka: no – probably not that reliably measureable).
That results in roughly 174mV at 20mA (at max gain of 47x). Arduinos can measure from 0 to 5V with 10 bits or 4.8mV. This ends up with roughly 30 measurements in 4 to 20mA. Not great precision.
Tl;dr: No. This is not the right way to measure the current output.
You can more easily measure your output with a precision resistor. Pass the current from the sensor through a resistor (say 100Ohm). That means at 4mA you have a voltage of 400mV across the resistor and at 20mA you get 2000mV across the resistor. You could measure this with the arduino directly, or if you wanted more precise measurements, measure it after amplification with an op amp or using an external adc.
See: http://forums.adafruit.com/viewtopic.php?f=8&t=12473