Leo is so desperate to protect others and disregards himself constantly. He does this so often (although poorly) that he rarely hesitates with any of his actions, leading to some... very good decisions!!!!!!!!! Even when it comes to being sacrificed, refusing for the sake of others, he never hesitates to make that decision... However, as Casey slowly starts breaking apart his entire world view up to this point, hesitation slowly starts to creep its way into his life, to the point where, for the first time, he hesitates when it comes to believing Splinter. He hesitates on his decision to be sacrificed. He hesitates as he sees the manifestation of Donnie's mind, terrified at the sight of him. He hesitates as the Shredder towers over him, unable to move or fight back or do anything.
Leo's desperation and hesitation are in constant battle with one another, as whilst he's desperate to continue his life mission and to continue on how he always has, he's now constantly hesitating in regards to his own beliefs and morals and if he's really making the right moves in accordance to them. Until his hesitation reaches its breaking point with the Shredder and leaves his desperation in the dust instead, now the emotion being overwhelmed.
I wouldn't say Leo was comfortable working off of his desperation, but more that he was practiced in doing so. This is what he is used to, this is what he must do, anything else must be ignored in his decision making process because any other emotion brings him too much into the focus of it and he is not the one he should be worried about. He's been a dead man walking his entire life. How his decisions affect him stopped mattering as soon as Splinter chose him.
It's a fair assumption in his case. He knows he's going to die, and soon at that. His life is already going to be an insignificant speck in comparison to those around him. May as well use it to the best of his ability. They deserve to have better lives than his.