It never actually says if they took it or not or if they even needed Szeth to do anything. Whatever their motives for killing Gavilar, getting a Shardblade at the same time seems like a good deal.
Sure, the Blade/Plate probably wasn't their main goal, but we can't say it wasn't one of their goals.
I think it pretty definitely wasn't one of their goals. How would they have managed it without specifically instructing Szeth? They're going to sneak someone else close to the king's body before any of his advisors get there to hurry and grab the Blade? No way. I'm sure they would have asked Szeth to steal the Blade if they had thought of it or fully understood what Truthless of Shinovar meant. They're probably not going to turn down a Blade if it comes their way (though they just might, since that is what they did by letting Dalinar and Adolin walk away, by fighting fair. They
might not believe in stealing an assassinated man's Blade), but they wouldn't sign a treaty and send an assassin that same night just for a Blade.
They wanted to kill Gavilar. They probably didn't think Szeth would even have to battle a Shardbearer to death. It was a surprise for Gavilar to be the one in the Plate, remember. They wanted Szeth to get the king, hopefully avoiding any Shardbearers along the way, but getting past them if he needed to.
There's no way they did all this to get one Shardsuit. It was not
the goal,
a goal, or even something they were hoping for.