For a some period of time at the beginning, yes. I think it was 7 months or so that he spent in alternating variants of suicide watch or prevention of injury status.

But for most of his pre-trial confinement he has been kept in the general population, and hasn't killed himself. Even after he plead guilty to charges that would have guaranteed him a sentence far worse than what Swartz would have received (even if Swartz had gone for a trial), Manning didn't kill himself.