Tain was a fool to try to invade the Dominion; a space they (Their secret force) didn't know. WIth him and the Romulans joining on a venture doesn't seem very Romulan to me, the entire story seemed out of character for both species. Yes, the Romulans would be pleased as well that I think species-WIDE, they can't make decisions that don't end with victory.
t's very possible that without a Founder on the Tal Shiar side, Tain's plan would have died in its first stages, long before the Obsidian Order built a fleet in Orias... without cloaking devices, Cardassian ships would have been picked off LONG before they got to the Founders' homeworld. And even though they got the location of it from the Romulans with the Federation deal for the Defiant, it would have taken them much longer to get that information through covert means. The entire plan hinged on the Tal Shiar working with Tain.
Also besides the fact Tain was seriously mistaken about the "white". He thought the Founders distributed the white to the Jem Hadar themselves. He thought, 'destroy the Founders, the Jem Hadar run out of white and die'. It was the Vorta that distributed it.
We found out later the Founders hardly ever interacted with the Jem Hadar. The Dominion could have still kept operating indefinitely - long enough to launch a major attack on the AQ.
And then there's the decision to join the Dominion, thinking that would all work out. Cardassians can be short sighted, and the Romulans are probably worse.
Seska's logic doesn't make sense and yet it does. The Kazon and Maj Culluh only wanted Voyager so they could beat their enemies. Not to explore ways to get Seska home. They don't even respect women in general.
And yet what Seska said does stand out--"if this were a Cardassian ship, we would be home now." You almost believe her when her says that.