So I assume you didn't try it yet. If you have a working system with the TL431, it should be not too difficult to test a LT1009.
If you assume there is virtual no current in the "ref" input, and the cathode-current versus cathode voltage (in the case the cathode is connected directly to the reference) behaves the same, you should be able to swap them.
On a larger scale , it doesn't matter how the component is made internally, if the behavior on the pins is more-or-less the same.
I've put the characteristics next to each other in following pdf. Be careful, the scale of the LT1009 is logarithmic.