will gfci work on ungrounded circuit?

I am certainly not the foremost expert, so my advice is just that. Ground Fault Circuit Interrupt trips the power when the current through the hot side of the circuit does not match the current through the neutral side of the circuit. This is an indication of a ground fault. (IE from the hot side through your body the water and metal pipe to ground)

With that being said, I am not sure how a missing ground would effect the circuit. Did you show the electrician the manual and ask him if it was just local code that prevents this type of no ground hook up?

 

Ground

If your electric box is metal you may be in luck. They are sometimes grounded. Verify by ohming out from the box to the nearest cold water line. Shut the power off to play it safe. Otherwise bite the bullet, open up the walls and run a ground wire from a fore mentioned cold water pipe. You'll be glad you did. While your at it get an electric socket tester. They're inexpensive, quick and easy to use.

 

A GFI circuit will work absolutely fine without a ground connection (this is terribly easy to demonstrate to yourself, but don't do it unless you know what you're doing). I don't understand why your electrician said you can't do it, unless he was quoting something from the legal codes applicable to your situation (you don't say what country you're in).

If you open up a GFI, you'll find the ground connection has absolutely nothing to do with the circuit operation. Inside, you'll find a current transformer that the hot and neutral (or two hot legs) run through. Normally, the current in these two lines cancel each other out and there's no signal to trip the GFI. But when the current is imbalanced, a signal is generated by the current transformer and when it's at or above 5 mA (typically), the GFI is tripped. You'll also see a second current transformer that's used to detect ground to neutral faults (in the US at least).