Do enlightened people "know" what nirvana is like?
Ud 8.1 says Nibbana is a sense object (ayatana) therefore it is obviously something known. 

MN 26 says:


  Then the thought occurred to me, 'This Dhamma that I have attained is
  deep, hard to see, hard to realize, peaceful, refined, beyond the
  scope of conjecture, subtle, to-be-experienced (vedanīya) by the wise.


SN 56.11 says:


  ‘This noble truth of the cessation of suffering has been realized (sacchikata).’
  
  
  
  Concise Pali English Dictionary sacchikata pp. of sacchikaroti
  realised; experienced for oneself.
  
  PTS Pali English Dictionary sacchikata seen with one’s own eyes,
  realized experienced


The Dhammapada says:


  205. Having savored the taste of solitude and peace (of Nibbana), pain-free and stainless he becomes, drinking deep the taste of the
  bliss of the Truth.


Nibbana is the dropping of all burdens; like the experience of relief when urgently urinating or dropping a heavy backpack or drinking cool fresh water on a hot day. 

Read more here: SN 43.14-43 and Nibbana For Everyone