No, it doesn't.
The Second Law of Thermodynamics is one of the most fundamental laws of nature: evolution really would be in big trouble if it contravened it. Put not particularly simply, the Second Law of Thermodynamics states that the entropy (the amount of disorganisation) in a closed system tends to increase with time. Put more simply, this means that matter does not tend to organise itself in a particular location unless there is some external energy source powering it. Evolution can be seen as matter organising itself.
Evolution-deniers who cite the Second Law of Thermodynamics as proof against evolution happening on our planet either conveniently forget to mention, or do not realise, that the earth is not a closed system: it has a rather massive external energy source, namely the sun. If we were to consider the entire solar system to be a closed system (which, to all intents and purposes, it is), then the occurrence of evolution on any of the planets would not break the Second Law of Thermodynamics, because, while evolution represents a local decrease in entropy, the burning of fuel within the sun represents a far greater increase in entropy—so, within the closed system as a whole, there is still an overall increase in entropy.
This is not a case of special pleading on behalf of evolution, by the way: the concept of a closed system is fundamental to the Second Law of Thermodynamics.