Time travel paradoxes are scientifically IMPOSSIBLE. They would violate the Copenhagen interpretation of quantum mechanics which states that you only get one outcome per event. Going back in time would violate that.
The fact that there appears to be nothing in physics to prevent backward in time travel, the apparent solution is the Everett/Wheeler hypothesis that allows for parallel universes.
If you're a B theorist, where past, present and future all exist simultaneously and everything always happens the way it did happen, is happening, and will happen, then yes. The paradox would not have happened in the first place and thus cannot occur because it never happened.
If you're an A theorist, where only the present truly exists, then no. However, true A theory doesn't seem to allow for travel into the past, which is what most people associate with paradoxes in time travel (since the past no longer exists).
Of course, there are many people whose beliefs in time fall somewhere in the middle; therefore, the paradox prediction would have to be adjusted accordingly.