The short answer is “Of course not.” A somewhat longer and more detailed answer is provided by an expert from the reality-based science community, Brian Cox.
Key statement (edited down to the relevant bits): “it’s absolute utter nonsense. It’s the biggest pile of [Laughs] shit that I’ve ever heard in my life. […] right there are two things to say; one is that it’s legitimate to ask the question. Every time you go to a new frontier and research be it biomedical research or high-energy physics, the question that should be legitimately asked - is this dangerous? Is there any risk at all? […] So then what about black holes? Well it’s just possible; there are extra dimensions in the universe and they set up just right that you could produce mini black holes at the LHC. That would be one of the signatures of extra dimensions. Now it’s extremely unlikely […] point because you know it requires the extra dimensions in the universe - but anyway; fine. You can make them. If that’s true then black holes are made in cosmic ray collisions with the upper atmosphere everyday because cosmic rays have energy far in excess of those that the LHC can create. So that means that […] there are black holes up there raining down on the earth all the time and they don’t do us any damage. […] Well the probable reason that we haven’t disappeared into a mini black-hole is because they don’t get created. Well let’s assume that they do; the next thing is that we have this prediction by Stephen Hawkings that they will decay away by a process called Hawkings Radiation which I might add is a much sounder theoretical basis than the extra dimension theories by which you could create these things. [Laughs] Anyway what if Hawkings Radiation doesn’t happen? […] Then you read on the web […] what happens if these black holes fly straight through the planet before they have a chance to eat it? Where is the one that the LHC could be created and just sit there and perhaps sink to the center of the earth? It turns out that when you do the calculation the black holes are so small that even if they didn’t decay and they just sat there they wouldn’t come close enough to any matter - because matter is basically empty space - to dissolve and to eat the matter and to grow so they wouldn’t do any damage. […] the final piece of wonderful evidence […] is that you look up into the sky and you see white dwarfs - some neutron stars - very, very dense stars. Cosmic rays are hitting those with energy greater than those seen at the LHC so if you can make black holes, black holes will be created on that surface. It turns out that they’re nuclear dense - these stars, so the black holes are not going to fly through there; they’re going to sit there and they’re going to eat away and they’re going to eat away much quicker than they could eat away the earth because the matter is much denser. So people have calculated how many neutron stars or white dwarves you would see in the sky if this were happening. If they were getting eaten by little mini-black holes and it turns out that there’d be very few indeed - in fact probably pretty much none […] there are layer after layer after layer […] of tests and some of them are observational and some of them are theoretical and it turns out that it’s utter nonsense.”