No, with mp_fadetoblack 0 you see THIRD-person-death, and with mp_fadetoblack 1 you see FIRST-person-death but with fading to black. So,
I suggest you to make cvar that changes the time of fading to black or at least removes fading to black at all.
BUT keeps FIRST-person-death.
EDIT: And maybe add cvar that adds fading to black on THIRD-person-death (mp_fadetoblack 0) with alterable fading time.
EDIT 2: I think this can be done with single cvar, something like
0 = keep original + remove the bug
-1 = do NOT fade
xx = fade xx second + remove the bug
Also I think it should not depend on mp_fadetoblack, just adds or removes fading.