I do not believe he will testify in the guilt/innocence phase or the penalty phase of his trial because that would open him up to cross examination, which he dares not risk. This does not mean, however, that he cannot speak to the jury. He has the right to allocution, which means he has the right to speak before sentence is pronounced. All defendants have this right.
In the first death penalty case that I tried, I had my client read a letter that he wrote to his daughter expressing regret for what he had done and for how that had affected their relationship. He broke down several times but eventually managed to get through it. The jury spared his life and several jurors told me afterward that they voted to spare his life because of his genuine tearful regret.
I am certain Judy Clarke and David Bruck have considered using allocution as a means for Dzhokhar Tsarnaev to speak to the jury about sentencing without being cross examined. Whether the tactic will succeed depends on whether he genuinely expresses remorse and regret.
The keyword is ‘genuine.’ Anything less and he will almost certainly be sentenced to death.