Dear Neil,
you can connect LEDs to ADC digital o/p.
and you can apply dc voltage within the input voltage range of ADC. you can adjut the scale of ADC.
now vary input voltage with the help of potentiometer.
calculate digital output bits theoritical.
and compare the digital out put of ADC just by noting on leds and off leds. i.e... 0s ad 1s.
this is the way you can check your ADC.

for testing you can write in software in your application itself.
forexample input ckt votage testing you just enter in tesing mode by defining the key.if input voltage is ok then it should shoe correct voltage with display.
for adcout put checking you can make your own instrument. say DAC with o/p voltage indication. for that in your existing circuit you shoud provide adc and microcontroller connection with FRC cable.
while checking just remove frc cable and put it in your test circuit.
and check the voltage on display.

Thats all.
Shashikant.