If an outlet has a ground terminal, it should be grounded. No ifs or buts. (And IMO, giving the illusion of ground protection is even worse than not having any protection.). I don't think you can even get two-prong outlets any more, so I think you'll have to fix the wiring. It sounds like you're still negotiating, so this is a good bargaining point. And if you don't get it fixed now, when it comes time to sell, any potential buyers would be within their rights to make you fix it then.
An easy way to check that your wiring has a ground conductor is to open up the service panel, look for the breaker that controls those outlets, then trace the black-shielded wire to where the cable feeds into the panel. (If it's present, ground is unshielded.)
If you have grounded wiring at the service panel, the next thing to check would be to look inside the outlets in question to see if the wiring there is grounded (it may just be a loose connection, and since it's common to daisy-chain outlets in a room, one faulty wire could affect several outlets).
If you have don't have ground at the outlets, but did at the service panel, you probably have a junction box joining the older ungrounded wiring and newer grounded wiring. Time to go exploring in the attic or crawl-space / basement.
GFCIs detect a difference between current going out on the live terminal and current coming in on the neutral terminal. If you're the easiest path to ground in an electrical fault, a GFCI will detect that and break the circuit; without a GFCI, you'd have to hope that you draw enough current -- and for long enough -- to trip a regular circuit breaker. On the whole, though, I'd rather that current was running to ground through some copper that's intended for just that purpose.
The best way to check for the bootleg ground, is to open up one of the boxes and look at how the receptacle is wired.
Since the grounded (neutral) and grounding conductors are bonded at the service equipment, they should always be at about the same voltage potential. If you had a long circuit, and an accurate meter, you might be able to measure a slight difference.
Since wire has a resistance, it's certainly possible to measure a voltage difference. However, a reading of 0 volts, does not necessarily mean there's a bootleg ground. The only way to know for sure, is to actually inspect the wiring.
Best Answer
You can use the tester below. If you touch one probe to the hot and the other to neutral or ground and the bulb should light.
If hot-to-ground lights but not hot-to-neutral the neutral is open. Vice versa for open ground. If you get nothing lighting either both neutral and ground are open or there's no power.
If hot-to-neutral and neutral-to-ground light, hot and neutral are reversed.
If neutral-to-ground and ground-to-hot light, but hot-to-neutral doesn't light, hot and ground are reversed.
It's a little complicated. Since there's no outlet hooked up you should probably just test to make sure the black-to-white and black-to-green light the light, if not there's a problem further down the line.
I mostly use this kind of tester to see which wires are hot in old work with cloth covered wires that you can't tell which color is which anymore.
It's also a handy tool to have to test all the wires in a box to make sure there's no power in any of them before you start touching them with your hands.