If you have totally balanced loading on your two phases you will not be able to detect any change. EDIT: Note that this is pretty much never going to be the case.
If you have a poor ground connection or the utility provider has a
poor ground connection you will have a floating ground. Unless
the neutral is bonded to a good local ground point it will float. It will
float in potential closer to the phase that has the heavier 115V
loads. If you have a 10A load on one phase and a 1A load on the
other phase you may find that the 1A 115V load sees 200V and the 10A
115V load sees only 30V. Electronic and reactive devices will
behave unpredictably at 200V or 30V if they are designed for 115V.
Resistive loads will dissipate more or less depending on the supply
voltage, over voltage will easily burn out transformers, globes and
motors, under voltage will also affect electronic power supplies and
synchronous motors that fail to get to speed.
can will be sharing the utility neutral until the point where the neutrals is are
bonded in the fuse cabinet. From this point it would be unwise to
share it for reasons like you describe but I can see it happening
when extra outlets are added with a mix of 115V and 230V without due
supervision. EDIT: The consumer is not expected to cope with a floating
utility side neutral or ground, it should never occur, in some wiring codes they
are bonded in the fuze box, in others the ground is local and the neutral comes
from the utility transformer common connected to the ground at the utilities transformer.
Sharing an local neutral
conductor between unbalanced loads is bad practice and not conformant to most wiring codes.
Below you can see how two dissimilar loads will cause the floating neutral point to be pulled from the earth reference if they share a neutral wire and it is compromised. In this example with the loads selected the larger load will be running at undervoltage (23V) and may survive if it is an incandescent lamp or heater but may fail if it is a motor or electronic load. The other load will see 207V and will likely suffer some failure no matter what sort of load it is.
It is also worth noting that the floating neutral point will be 92V above the protective earth, if any, in this example.
simulate this circuit – Schematic created using CircuitLab