An annulment can be made on the basis that a couple did not have sexual relations.
However!
In as far as Irina and Jack go, we know that
this is not the case! Jack states that he can have the marriage annuled on the basis of
fraud because Irina
misrepresented her identity. Until he has the marriage annulled, they are still
technically married, as he stated (I suppose Irina could also have it annulled).
If they had not had sex, Jack would most certainly have known
immediately, many, many years ago that something was severely wrong with the marriage and there would be no discussion of either Irina Derevko or Elsa Caplan having "prostituted" themselves. Jack thought that he was in a very happy, blissful marriage, which, pardon me, would most definitely
not be the case if he weren't, well, "getting any" on a regular basis.