No, in a Jack Finney-H.G. Wells sort of way. OBAFGKM already showed you that if Alice sends an FTL signal (event "A") to an observer Bob (event "B"), and Bob is travelling towards Alice sufficiently fast, event "B" will occur before event "A" in Bob's frame. That means that in Bob's frame, his line of simultaneity intersects Alice's location at an earlier time than she sent it. So if Bob bounces this FTL signal back to Alice, it will arrive at her location before she actually sent it.