No, he wouldn't. Not really, but again, he just knows that he's a hostage and Chaoji was hurt in such a way as they don't know if he'll make it or not.

"Knowing each other for years doesn't mean that you're close." Lavi shifts more on the bench until his head is resting on the seat itself, ignoring Tyki's presence further. "And the name is 'Lavi' not 'eye-patch'."