Well, I'd say there's a significant chance you'd end up with a boom instead, for invoking the (quantum) chronology protection conjecture.
That wouldn't necessarily stop you in all cases, though. It just means you need quantum computer-level isolation, or a signal that doesn't include any actual closed timelike curves - that is, you could hypothetically send a signal from 2011 Earth to 2006 Alpha Centauri so long as the response takes five years to get back.
Hmm, I don't think most variants of chronology protection imply inherently destructive results. But your remark made me feel all of a sudden very worried that if is real this could be connected to the Great Filter. I'm almost certainly assigning this more emotional weight than the very tiny probability that is at all justified.
http://www.nature.com/news/2011/110922/full/news.2011.554.html
http://arxiv.org/abs/1109.4897v1
http://usersguidetotheuniverse.com/?p=2169
http://news.ycombinator.com/item?id=3027056
Perhaps the end of the era of the light cone and beginning of the era of the neutrino cone? I'd be curious to see your probability estimates for whether this theory pans out. Or other crackpot hypotheses to explain the results.