I noticed with a two wire cable (with a ground), the ground and neutral wires in the circuit breaker box all connect together. If I have a two wire only cable to a new three wire receptacle can I install a jumper from the neutral to the ground terminal in the receptacle box with the same results?
Although the neutral wire will generally be near ground potential, there are some situations where it might not be. For example, when switching on a large motor, the voltage on the neutral wire may jump briefly but significantly. Further, if the neutral wire breaks between a device and the panel, it will very likely end up with full line voltage on it. If the neutral wire were bonded to the ground terminal on a piece of equipment, any voltage on it could shock anyone touching the equipment. Because the current would be flowing on the ground wire which the ground-fault interrupter does not switch, the GFCI would provide no protection against it.
The accepted way to handle the situation where no ground is available is to use a GFCI with its ground lead attached to nothing but with a label affixed reading "NO EQUIPMENT GROUND". A GFCI used in such fashion will not detect some failure modes that would be detected if the grounding wire were bonded to neutral but the danger of putting neutral voltage on the ground wire exceeds the safety gain from catching those particular failure modes.
It would be helpful if someone were to sell a GFI which was designed to connect ground to neutral well enough to trip the detector immediately if a device has a leak between its hot and ground leads, but not well enough to pose a dangerous condition. I am unaware of any such devices being for sale, however.
Short answer: NO
Bonding the neutral and the ground anywhere but the service is prohibited.
This puts neutral current on the ground wire that people expect to be safe under normal conditions.
I know they go the same place, but they serve two completely different functions.
Long story short, if you have no proper source of ground, then the proper choice is to use a GFCI with no ground bonded at all.
Why this is okay is interesting though:
Suppose you have a metal tool with a ground fault. If you are totally isolated from any grounding conductor while using the tool, you will never know it has a fault. Once you become grounded, then the GFCI will sense a fault and trip.
The only real difference you would see between the two scenarios is if the fault is really low impedance. If there were a proper ground, then the breaker would trip immediately with an arc at the receptacle when the tool was plugged in GFCI or no. Now you will not get that immediate shut off. Instead either you will become part of the path and the GFCI will trip, or you will place the tool against something grounded, at which point there will be an arc at the tool and the breaker will trip.
So it's not as good having a ground conductor, but it's acceptable (and it meets code requirements) to install that way. But ONLY if there's no ground available at all. That is to say that you can't skip wiring the ground just because.
[EDIT] As Hot Licks says in the comments, make sure to label the receptacle that it is not grounded. :)