No, the only way for something to survive is if the half life model breaks down and the chance of decay during different time periods isn't independent. This would be the case if one of the strands was somehow preserved accidentally.
That half-life is the time it takes for the link between half of the bonds between nucleotides to break (http://www.nature.com/news/dna-has-a-521-year-half-life-1.11...)
So, after 1042 years, only a quarter of the bonds will be intact. After 100 million years, only 1 in every 2^190000 bonds will be expected to still be intact. Taking 2^10 = 1000, that's 1 in every 10^57000. I think that's quite a bit higher than our estimate for the number of particles in the universe (https://www.quora.com/How-many-particles-are-there-in-the-un...)
TL/DR: I wouldn't bet on it.
[1] - http://www.calculator.net/half-life-calculator.html?type=1&n...