Will an ungrounded light fixture on a GFCI circuit cause the GFCI to trip?
This is a common misconception when using Ground Fault Circuit Interruption (GFCI) devices.  GFCI devices do not require an equipment ground to function, they detect unbalanced loads within the circuit using the "hot" (ungrounded conductor) and the "neutral" (grounded conductor). 

In a properly functioning circuit, the current on the ungrounded conductor and grounded conductor should be equal.  

You can test this yourself, using a clamp on ammeter. If you clamp the meter around both the hot and neutral wires, you should read 0 Amps (If you read anything other than 0, you have current leakage). This works because the current flowing through the wires creates an electromagnetic field, and since the current is flowing in opposite directions the fields cancel each other out.

A GFCI device takes advantage of these principles, and is able to detect current leakage by comparing the current on the ungrounded and grounded conductors.