I think this is missing the elephant in the room, namely that you need to have selection (natural or otherwise) for evolution to happen (in a reasonable time). And selection (unlike mutation) is not a local operation on the DNA strands as required by the data processing inequality. Selection tosses out some individuals carrying certain strands in relation to others carrying different strands. The "comparison" performed by selection is not a local post-processing operation (as required by DPE to apply) on a single strand/individual; it takes two or more things to compare them...
The more relevant math for evolution is the Price equation, which partitions the change in fitness in that due to selection and transmission causes (like mutation, recombination etc.) If there's no selection, you're left just with the transmission causes. And in your case the single-individual/strand post-procession would be just mutation. What your math is saying is that not much evolution is likely to happen by mutation alone. (Also, you are taking evolution to mean an increase information/complexity rather than in fitness, but that is a lesser sin. An elephant with 500 legs isn't necessarily the most fit in many environments.)
Given your stated interest in ID, I have the feeling you're dressing up with math a common misconception/argument used by ID proponets, namely that complexity is unlikely to occur via evolution; usually the ID propoents jump to that conclusion by misrepesenting (or misunderstanding) the evolutionary mechanims (as you have done here). Your question reminds of this common ID argument:
Assume that, at each mutational step, there is equally as much chance for it to be good as bad. Thus, the probability for the success of each mutation is assumed to be one out of two, or one-half. Elementary statistical theory shows that the probability of 200 successive mutations being successful is then (½)^200, or one chance out of 10^60. The number 10^60, if written out, would be "one" followed by sixty "zeros." In other words, the chance that a 200-component organism could be formed by mutation and natural selection is less than one chance out of a trillion, trillion, trillion, trillion, trillion! Lest anyone think that a 200-part system is unreasonably complex, it should be noted that even a one-celled plant or animal may have millions of molecular "parts."
The evolutionist might react by saying that even though any one such mutating organism might not be successful, surely some around the world would be, especially in the 10 billion years (or 10^18 seconds) of assumed earth history. Therefore, let us imagine that every one of the earth's 10^14 square feet of surface harbors a billion (i.e., 10^9) mutating systems and that each mutation requires one-half second (actually it would take far more time than this). Each system can thus go through its 200 mutations in 100 seconds and then, if it is unsuccessful, start over for a new try. In 10^18 seconds, there can, therefore, be 10^18/10^2, or 10^16, trials by each mutating system. Multiplying all these numbers together, there would be a total possible number of attempts to develop a 200-component system equal to 10^14 (10^9) (10^16), or 10^39 attempts. Since the probability against the success of any one of them is 10^60, it is obvious that the probability that just one of these 10^39 attempts might be successful is only one out of 10^60/10^39, or 10^21.
All this means that the chance that any kind of a 200-component integrated functioning organism could be developed by mutation and natural selection just once, anywhere in the world, in all the assumed expanse of geologic time, is less than one chance out of a billion trillion. What possible conclusion, therefore, can we derive from such considerations as this except that evolution by mutation and natural selection is mathematically and logically indefensible!
Which has been (easily) debunked before:
This is a rather simplistic attack on evolution by mutation and natural selection. The way that he is calculating the probability actually does not take into account natural selection. What he is calculating is the chance that 200 random beneficial mutations happen sequentially without any bad or neutral mutations happening between the beneficial mutations. Natural selection will select and preserve the beneficial mutations and select against and eliminate the bad mutations. Once a beneficial mutation has become fixed in the population, any offspring produced that changed this would be selected against. His example also has no basis in a known biological system. His model essentially has an organism that reproduces only one offspring and then dies. All biological systems known to me the organisms on average have more than one offspring, allowing multiple chances for unique mutations to happen for selection to act on. Even using his unrealistic model slightly modified to have more than one offspring with adding in Natural Selection and having it take 2000 generations for a single beneficial mutation to fix in the population it would take ((2000 generations) * (200 fixed mutations)) = 400,000 generations to get the 200 fixed mutations, which with a generation time of 0.5 seconds would take about 2.3 days. If we use his numbers of one mutation per generation with a 1/2 probability of being beneficial, which would equal to a fixation rate of beneficial mutations about once every two generations much more generous than my 2000 generations. We do the same calculation with these numbers we get (2 generations) * (200 fixed mutations) = 400 generations, which is about 3 minutes.
tl;dr: The guy is an idiot.
For a more academic discussion of this argument see "There’s plenty of time for evolution". The gist of that paper is
The fact is that with the parallel model, i.e., taking account of natural selection, the number of rounds of mutations that are needed to change the complete genome to its desirable form are only about K log L, instead of the hugely exponential K^L which would result from the serial model.
where L is the length of the genomic “word,” and K is the number of possible “letters” that can occupy any position in the word
For a broader treatment of information theory issues in ID vs evolution see Elsberry and Shallit; an older version of that paper can be found freely on teh interwebz.