Not sure what the laws are in NJ, but in Texas irrigation contractors are required to have a minimum of 6" coverage between irrigation piping and top of grade. UNLESS... (there's always an unless), you are are in areas where there are obstructions such as roots, piping, etc. Then you are required to have at least 2" inches of coverage.

I'm not sure what core aerator you are using nor the depth. Probably somewhere in the 4" range or shallower. For a normal installation I would probably say you would be OK, but considering you said that there were areas where the contractor had to go shallow to avoid piping, you may run into some problems. Aerating the yard but avoiding these shallow areas is always an option, although it will probably not provide the look and results I think you are after.

I would suggest contacting the contractor who installed your irrigation system and explain to them what you are wanting to do and see if they forsee any problems. They would know better than anyone how deep the pipes were laid. But I wouldn't expect them to take responsibility for any damages incurred by you aerating your lawn. Like I said, laws differ from state to state, but I'm sure that they have exceptions to minimum depths similar to Texas. As long as his minimum depths are within the states requirement, then any damages incurred from the homeowners actions would make repairs the owners responsibility to correct.

Good Luck

Here is a link that might be useful: EvergreenSprinklers.com

Mark your heads and avoid. Lines should be down 7 - 9 inches, way below the depth of a core aerator plug.