Aardwolf, any form of FTL can be functionally equivalent to time travel. There are no exceptions.
Except, conversely, every form of FTL forms a time-space path from point A to point B which isn't dependant on the observation cones based on the assumption that speed of light is the fastest speed information can propagate through time and space.
Or, in other words, if you FTL from point A to point B, you're not actually moving through the space between the points at superluminal speed, you're making the distance shorter - depending on type of travel, the distance via FTL travel can be anything from astronomical units (Star Wars hyperspace) to order of thousands of kilometres (Babylon 5 hyperspace) or just kilometres (FreeSpace subspace) to zero (BSG type FTL jump drives).
FTL can't reverse causality, it just introduces a way for information (and therefore causality) to not be bound on the observation cones that are so commonly used to create "paradoxes".
General Relativity doesn't exclude the possibility of information travelling faster than speed of light in vacuum. It simply states that it is impossible for an object with rest mass to be accelerated by a force to speed of light when confined to the currently known time-space continuum.
Now, what comes to Alcubierre drive in which there technically is no force accelerating the ship, but space-time itself moving the ship on a wave... well, even then it's possible that waves in space-time continuum propagate at speed of light at most, in which case riding the wave wouldn't still quite bring you to superluminal speeds.
Except if you take into account time dilation. Which you can also interpret as making the way shorter rather than ship faster...