ADCs like the LTC2323 have an internal reference that is available at REFINT1/REFINT2 pin.
Can I tap this pin externally to use this voltage in external circuitry? If yes, how much can I drive it (load resistance/cap, current)?
The datasheet is unfortunately very silent on that. It does not explicitely state that it can be used externally but that it is "available at REFINT1", suggesting it can. Furthermore, it states the output impedance as 0.25 Ohm.