Would this design carry too much current and damage battery charger ICs?
will each battery charger IC only pull the required 500mA of current
  from the main supply line?


Yes.


  Will this design work, and can it scale to even larger numbers?


Yes, so long as the power supply wires are thick enough to handle the current without excessive voltage drop.


  Would a person touching the main line risk getting electrical shock?


No. 5V is not a high enough voltage to cause an electric shock. However if the supply rails are exposed then they could be shorted out by a metal object (eg. a ring or bracelet) which could heat up or even vaporize if the available current is high enough. 

For safety and to reduce wire size you might consider splitting the supply line into several sections, each with its own feed wires from the power supply. Each section could also be separately fused at a current not much higher than the maximum number of chargers in it. For even better protection you could put a fuse in line with every charger, then if any one shorts out it won't affect the other chargers.