It is not essential, but wise, to know which is live and which is phase because most of time only the phase line has a fuse.
The scenario is:
Get a short circuit to case and you touch it (providing a path to gound) you get a good tingle
.
Fuses also protect your equipment from being cooked.
If you are attaching additional equipment to the existing AC line and don't know which is which wire, put fuses on both wires and you will be safe.
Remember that a fuse may blow with 5A whereas your power-boards fuse is more likely to be 30A+ (for example)