A closed time-like curve is defined as a word-line that returns to its starting point, in the $x$, $y$, $z$, $t$ coordinates. So, for a chronology respecting observer, an object traversing a closed time-like curve would appear to violate causality. Under certain conditions (Tolman et al.), superluminal propagation of signals also appears to violate causality. Does this indicate that for a tachyonic anti-telephone situation, the worldline of a superluminal tachyon could be considered as a closed time-like curve?
No. The world-line of a tachyon is spacelike. That's the definition of a tachyon. That means it can't be a closed timelike curve.
The existence of CTCs is a property of the spacetime, not of the particles inhabiting it. Minkowski space simply doesn't have CTCs.