If for some reason the neutral touch the ground (eg : detached wire in some electric appliance), and some current flow trough the ground, what happen to the electric meter, will it be able to measure that current flow ?
We assume no GFCI is installed (otherwise AFAIK it should trip immediately)
I think there is two cases :
1) some current flow between neutral and ground because there is some potential difference between the two (AFAIK in theory it should be zero but there can be a difference between the ground of the house and the one where the place where the 3 phases are transformed to 3 phases + 1 neutral, using a delta wye transformer).
2) some current flow between live and ground instead of live to neutral because some appliance is connected (eg : electric heater).
For case 1) and 2), let's say I have 5A flowing, what will happen to the electric meter ? will it be able to measure that current (or is it only able to measure live/neutral) ?
Here is some meter schematic I found :

There is 3 coils : one directly between live and neutral and two other ones in series with the load.
Unfortunaltely it does not tell which side is live or neutral (but does it really matter?)