How to drive an LED with an LED driver
Yes, you should care. The BCR421 will try to maintain a (roughly) constant current at the collector terminal, however if Vout drops too low then it will not be able to maintain the constant current, as you can see from the graphs you posted. What will happen is that the output will saturate at a lower current than you want. To find out if this will happen, assume that the maximum desired current is flowing through the LED. Subtract the maximum possible LED voltage (which will occur at the maximum current) from the minimum possible supply voltage and compare with the dropout voltage of the BCR421 at that current. 

So the LED drops 1.35V typical at 100mA (1.6V maximum). Your supply
voltage is 3.3V nominal, let's dock 5% for tolerance to give 3.13V.
That gives the chip 1.54V to work with. The parameter VSmin
indicates that typically 1.4V is enough at 25°C, and the graphs you
posted indicate that above about 1.1V it's fairly constant current.
So it's likely okay unless you have some extreme operating
conditions.
The current through the external resistor when it is regulating correctly will be approximately Iout - 10mA. The internal resistor conducts the 10mA. It will be slightly higher because of base current (maybe 0.5%), but that's immaterial in this situation, given the +/-10% tolerance on the 10mA current. As @jippie points out in a comment, 100mA through a pot wiper is probably not a good idea, depending on the pot construction (okay for a wire-wound, but they are expensive). Minimum resistance may also be a problem. It's generally recommended not to put much current through pot wipers- they work better as voltage dividers than rheostats. 
This circuit maintains a fairly constant current regardless of changes in the LED forward voltage (or differences from unit-to-unit when first assembled) and regardless of changes in supply voltage.