How much of a deficiency of iron need be present to start pica?

No specific level. Not everyone with low serum (blood) iron level shows pica. Some may start showing pica with just a marginally low level, others won't until it is extremely low. Not everyone with pica has an iron deficiency.Pica can occur because of 'cravings', hunger, anemia, and other reasons. The june 2012 issue of scientific american has a brief article about this very topic.
No correlation. Pica is the consumption of non-nutritious material. It can start for lots of reasons, but is not correlated with a specific level of iron deficiency. If you think you have anemia or are suffering from pica, please see your doctor.