Mace would've viewed that message as confirmed all the bad stuff about Anakin. Ahsoka doesn't trust the Order to do the right thing because they betrayed her, they assumed the worst, and she thinks they would do the same. When Anakin went to Mace, Mace said if it was true, then Anakin would've gained the trust of Mace, and Mace had him wait in the Temple. I'm not sure how the interaction would've changed much.
Only way I see it changing is if they sent someone else to Kashyyyk and it was Yoda that worked with Anakin after learning that Palp was after Anakin. Anakin helped Yoda escape when Yoda went on his quest that Qui-Gon sent him on. Because of that, Yoda might be the only one that can understand and isn't purely focused on the war.
Sending Yoda away was part of the Jedi strategy to draw out Sidious. The Jedi felt that with Yoda off planet that maybe Sidious would make his move sooner because he felt safer. They assumed that Mace could handle it. It was part of the arrogance of the Jedi.
If you go back and read the ROTS novel which was excellent. Yoda realized the failings and arrogance of the Jedi at the end of the duel with Sidious.
Basically Yoda realized that when the Sith disappeared that they had spent that time re-inventing themselves. They went from power mad Dark Force users that created huge armies and tried to conquer the galaxy through might and who would constantly self destruct due to their hunger for power, to being focused on growing more and more powerful in the force, learning all aspects of it including their enemies the Jedi and learning guile and patience.
the Jedi on the other hand kept preparing to face the Sith from thousands of years ago. By the time Sidious came along he was insanely powerful because he had continued to grow on the strength and knowledge acquired by the Sith over thousands of years. On top of that the Dark Lord that Yoda faced had been a supreme planner who not only created the ultimate jedi trap, but had undermined the Jedi's power and ability to use the force.
As Yoda was fighting Sidious he realized that he just didn't have the power or training to beat Sidious head on. He couldn't beat someone that was basically the embodiment of the Dark Side of the Force.
During the Mace Anakin fight, in the ROTS novel, Mace didn't trust Anakin, but he did strongly believe that Anakin would always come down on the light side of the Force, again that Jedi arrogance.
What was funny was there was a line that Sidious used in the novel that should have made its way into the movie.
As Sidious lay beaten and burned at Mace's feet, Mace kind of sneered at Sidious and said something like "You're a typical Sith, I can feel the fear in you". And Sidious laughed and told him that the fear he felt wasn't Sidious'. It was Anakins fear of losing not only Padme, but losing Sidious. If Mace would have been forewarned by Ashoka about Anakin, he might not have been taken off guard by Anakin's fear based response.
. I give it a pass though because it's in the same timeline where ships can fly at the speed of light. Really looking forward to the finale. Love that we only have to wait three days rather than a week. 
