What are the consequences of Brutus not taking Cassius's advice to let Cicero be part of the conspiracy in Julius Caesar?

Cicero is killed in Antony’s proscription. 

Cassius seeks out Brutus to join his conspiracy against Julius Caesar because he feels that his name will lend them legitimacy.  Brutus takes the position seriously.  He takes charge right away, and when the conspirators join him at his house he makes it clear that he is in charge.  One example of this is his reaction to Cassius’s suggestion that Cicero be included. 

CASSIUS

But what of Cicero? shall we sound him?
I think he will stand very strong with us. (Act 2, Scene 1) 

There is a big discussion about whether or not Cicero should be included in the conspiracy.  After Cassius suggests him, Casca and Cinna are all for it.  Metellus Cimber says that “his silver hairs/Will purchase us a good opinion.”  They seem to think that people trust Cicero’s opinion, and with him seeming to lead the group people will be more likely to follow them. 

Brutus does not like this idea.  After all, he wants to be in charge.  He doesn’t want Cicero telling him what to do.  Cicero was a very important person in Rome.  He could threaten Brutus’s authority. 

BRUTUS

O, name him not: let us not break with him;
For he will never follow any thing
That other men begin.

CASSIUS

Then leave him out. (Act 2, Scene 1) 

Brutus is basically saying that Cicero would not go along with them because it wasn’t his idea.  The conspirators therefore do not include Cicero, even though he might have been on their side. 

Clearly, Antony thinks that Cicero is a supporter of the conspirators.  He has him proscripted when the triumvirate is preparing for war against Brutus and Cassius.  Brutus and Cassius are horrified to learn that Cicero has been killed. 

BRUTUS

Therein our letters do not well agree;
Mine speak of seventy senators that died
By their proscriptions, Cicero being one.

CASSIUS

Cicero one!

MESSALA

Cicero is dead,
And by that order of proscription. (Act 4, Scene 3) 

Cicero wasn’t saved from death by not being part of the group.  He is clearly seen with several of the conspirators, so Antony would have thought he was one of them.  If he had been part of the group, he might have gone with Brutus and Cassius and would not have been killed in the proscription, but of course he might have been killed or committed suicide later.

The incident with Cicero shows how badly Brutus wanted to be in charge.  He did not take Cassius's advice on this or many other matters.  If Cicero had been with them, he probably would have taken charge.  This would not have been a bad thing for anyone but Brutus.  Cicero was respected and was a renowned public speaker.  Things might have gone differently for the conspirators if they had Cicero speaking publicly for them, rather than Brutus.