I recently have acquired stained and freezed cells on flowcytometer, and i found no difference, still i prefer to fix the stained cells if i am going to acquire the sample in a week or so.
But few people use this freezing-stain-acquisition protocol in their lab, and it works.
Jaksztat has published the effect of freezing on cells from sputum for flowcytometry.
Article Effect of freezing of sputum samples on flow cytometric anal...