I am using the Schott 22523 surface mount transformer. It comes in a 6 pin package and according to the data sheet pins 2 and 5 look like they connect to the core. Is my understanding of the datasheet correct? What is the purpose of allowing someone to tap into the core?
They are not to the core itself but a screen between the primary and secondary winding. It is to give better screening between each side and helps eliminate capacitive coupling between them.
Yes, always connect it to ground. The magnetic coupling between the windings still works as before but capacitive coupling is prevented because it has to pass through the grounded connection between them.