The best answer I can compose is – we can’t know about every case, but generally not.
There were many good reasons to not kill old or disabled slaves. They could be given very light work to do; they could teach their skills to younger slaves; they could join the “house slaves” if physically able (with the advantage of not being a threat to the family), they could provide care and supervision for children too small to be put to work and/or for the white children. Moreover, a slaveowner who made a regular, standard practice of killing his slaves would face considerable threat, both of his remaining slaves trying to flee or possibly in desperation killing him instead.
Slavery was a brutal and dehumanizing system, but the whites who lived on large plantations were quite conscious of being outnumbered by their slaves, and there was a fine line between enough fear to maintain control and so much as to provoke dangerous or desperate resistance.
Probably some slaveowners did kill old or disabled slaves, as some also occasionally killed healthy ones. But most would not have, for reasons of their own conceptions of humanity as well as out of self-interest.
George Washington repeatedly reduced the responsibilities of his most elderly slaves and complained about how much they cost compared to how much they could produce – but he did not harm them and sought to see to it that they were cared for.