Can you develop an immunity to chopping onions causing tears?
Given that the tear-causing effect of onions is due to a straight forward chemical process, it seems highly unlikely that you would develop any kind of actual immunity in terms of the effect.  Scientific American describes it:


  Peeling, cutting or crushing an onion's tissue releases enzymes called
  allinases, which convert these molecules to sulfenic acids. The
  sulfenic acids, in turn, spontaneously rearrange to form
  syn-propanethial-S-oxide, the chemical that triggers the tears. They
  also condense to form odorous thiosulfinates, coincidentally evoking
  the pungent odor associated with chopping onions and eliciting the
  false accusation that it is the odor that causes the weepy eye.
  Incidentally, sulfenic acid in garlic takes a different chemical
  route, sparing the eyes. The formation of syn-propanethial-S-oxide
  peaks at about 30 seconds after mechanical damage to the onion and
  completes its cycle of chemical evolution over about five minutes.
  
  [ ... ] Free nerve endings [on the cornea] detect
  syn-propanethial-S-oxide on the cornea and drive activity in the
  ciliary nerve--which the central nervous system interprets as a
  burning sensation--in proportion to the compound's concentration. This
  nerve activity reflexively activates the autonomic fibers, which then
  carry a signal back to the eye ordering the lachrymal glands to wash
  the irritant away.


It turns out that newer science indicates the conversion is not spontaneous, but due to an enzyme for this purpose, now named lachrymatory-factor synthase.  

What is likely, especially for an experienced cook are:


Improved knife skills and speed, lowering the amount of time in close contact with the irritating gasses produced by chopping onions
Increased tolerance for the specific sensation