Well Arc is a GIS system, and it doesn't really "like" coordinates just out there floating in space.
The projection or coordinate system tells Arc what these XY numbers mean and define its relationship with a model of the earth. Where it is actually located.
So, you could set up a dummy local projection or use a standard TM, with an arbitrary central meridian, latitude of origin etc.
So if you made these both 0, 0, your data would out there floating in the gulf of Guinea, off the Nigerian coast.