No, setcc actually does depend on the previous value of the register, because it only comes in the low-byte variants (i.e. al, bl, cl, dl etc)--the top 7 bytes of the destination are left unmodified.

A one-instruction variant I've seen that gets you the negated value of the carry flag is sbb rax, rax. This doesn't depend on the previous value of rax in a mathematical sense, though I'm unsure if it depends in an out-of-order sense; that is, if it's recognized as a zeroing idiom (or rather, zeroing or all-one-ing in this case). Probably not.

EDIT: did a quick test, and sbb rax, rax etc are not recognized to be a zeroing idiom, at least on my old Haswell. So it's still one instruction, but has a dependency on the previous register value.