The episode only works if the Romulans find out the truth after the Dominion War and declare war on the Federation. The writers wimped out by not showing that.
Sorry to add a late reply, but there is a subtle discussion of Romulan perceptions of Vreenak's demise in Una McCormack's Treklit sequel to the episode, Hollow Men
More to the point, Hollow Men
is a wonderful examination of espionage in Trek, as well as the Sisko's guilt and sense of honour, the utilitarian attitudes of Starfleet (& S31) during war and, most of all, McCormack's excellent recurrent treatment of Garak (see also the Never-Ending Sacrifice
and The Lotus Flower