In Julius Caesar, is Brutus willing to surrender if the conspirators lose the battle against Antony and Octavius?

Brutus is not willing to surrender. When Cassius asks him in Act 5, Scene 1, if he would be content with Antony and Octavius leading him in triumph through the streets of Rome if they should lose the battle, Brutus replies:

No, Cassius, no: think not, thou noble Roman,
That ever Brutus will go bound to Rome
He bears too great a mind. But this same day
Must end that work the ides of March begun;
And whether we shall meet again I know not.
Therefore our everlasting farewell take:
For ever, and for ever, farewell, Cassius!
If we do meet again, why, we shall smile;
If not, why then, this parting was well made.

Brutus equivocally states he is too great a man to suffer the dishonor of being led through Rome as a prisoner. These words are, however, inconsistent with what Brutus said when he spoke out against Cato's suicide, calling it "cowardly" and "vile." It is clear Brutus deems the disgrace of being displayed as a failure a greater dishonor than suicide. He would rather take his own life than be humiliated in such an ignominious manner.

Lucilius later confirms Brutus' determination when Antony asks him about his whereabouts in Act 5, Scene 4. Lucilius responds by saying,

Safe, Antony; Brutus is safe enough:
I dare assure thee that no enemy
Shall ever take alive the noble Brutus:
The gods defend him from so great a shame!
When you do find him, or alive or dead,
He will be found like Brutus, like himself.

He means Brutus will retain his honor and will be found in death as he was in life. Brutus's death will not be that of a coward, but of a noble lord who sacrificed his life for the good of Rome.

When Brutus realizes the battle is lost in Act V, Scene 5, he asks Volumnius to hold his sword so that he may run onto it.

Nay, I am sure it is, Volumnius.
Thou seest the world, Volumnius, how it goes;
Our enemies have beat us to the pit:

Low alarums

It is more worthy to leap in ourselves,
Than tarry till they push us. Good Volumnius,
Thou know'st that we two went to school together:
Even for that our love of old, I prithee,
Hold thou my sword-hilts, whilst I run on it.

Volumnius refuses and Brutus later asks his attendant, Strato, to do the same:

I prithee, Strato, stay thou by thy lord:
Thou art a fellow of a good respect;
Thy life hath had some smatch of honour in it:
Hold then my sword, and turn away thy face,
While I do run upon it. Wilt thou, Strato?

Strato complies with his request and Brutus kills himself by running onto his sword stating, before he dies, that he had less of a desire to kill Caesar than he had in that moment to kill himself.

Caesar, now be still:
I kill'd not thee with half so good a will.

Brutus' suicide ties in well with the promise he made to the crowd in the marketplace after Caesar's assassination in Act 3, Scene 2. On that occasion, Brutus declared at the end of his speech:

With this
I depart,—that, as I slew my best lover for the
good of Rome, I have the same dagger for myself,
when it shall please my country to need my death.

And so, it came to pass. Brutus, an honourable man, chose to die with honor rather than be led through the streets of his beloved Rome like a slave.