Spoiler: This is so spoiled it gets a new car every year.Without Rogue One, Vader claims that they had transmissions beamed to that ship by Rebel spies, and Leia tries playing innocent. The Senate could be sympathetic to the rebellion if the Empire is pulling over senators without sufficient proof.
With Rogue One, Leia is provably part of a Rebel fleet that participated in an attack on an Imperial base, where Imperial soldiers died. Even if she gets in front of the senate and screams, "Death Star!" at the top of her lungs, she'd be openly admitting to committing treason.
Senators being arrested with no proof (no Death Star plans found anywhere) generates sympathy in the Senate. Senators confessing to treason does not.
The Shaggy defense is not desperate. It's tone deaf. It's saying, "I'm not going to do a damn thing to help myself and instead will just hope and pray the other side manages to mess up somehow."