If NF is consistent, then yes Con(NF) would be one of these statements that are independent of NF. NF can interpret finite order arithmetic, so by that it would be subject to Godel incompleteness theorems. If Randall Holmes's [proof][1] of Con(NF) is correct, then NF is slightly stronger than finite order arithmetic, this means that all [strong axioms of infinity][2] are independent of it. 

OF course as regards NFU (which is equi-interpretable with SF (the theory with the single schema of stratified comprehension)) the matter is settled, its incomplete for the same reasons, it's not even complete for stratified statements of its language since it cannot prove infinity. Actually even known *consistent* weakening of NF to only three types "NF3" or to only using predicative formulas "NFP" (or mildly impredicative ones "NFI") are also incomplete! With known independent results [see [here][3]]

 


  [1]: https://math.boisestate.edu/~holmes/nfproof/newattempt.pdf
  [2]: https://en.wikipedia.org/wiki/New_Foundations#Strong_axioms_of_infinity
  [3]: https://en.wikipedia.org/wiki/New_Foundations#The_consistency_problem_and_related_partial_results