If there is an adjustment in valuations across the industry, 
  it should not effect the public markets the way it did in 2000. 

Isn't this only in the case where the said unicorn is not IPO'd. Like in the case with Groupon which lost 85% of it's value since IPO, the public market is affected.

If these 59 unicorns go public and begin to loose money, they would effectively trigger a domino I believe.

Like the VCs who get in during the E/F rounds, the general public is also susceptible to similar behavior.