Permacomputing

Yes, but I don't know how much (and it would vary based on numerous factors).

An uncompressed format would need 3,117,275,501 X 2 bits to be able to guarantee that it can encode any DNA sequence of 3,117,275,501 base pairs (caveats and nuances aside).

However, human DNA sequences aren't completely random! There are constraints on what would actually be a valid human DNA sequence. That opens the possibility of compressing the data.

For example, you'll never find someone with 3,117,275,501 of exactly the same base pairs (i.e. AAAAAAAAAA....AAAAAA), it's impossible. Based solely on that, you don't actually need all 3,117,275,501 X 2 bits of information. In fact, the set of valid human DNA sequences is probably considerably smaller than the set of all possible DNA sequences of the same size (can't find any specific data here, so you'll just have to "trust me bro"). So, a good/smart algorithm can make use of that to generate representations that require fewer bits of storage.

Another aspect of human DNA is that it contains a lot of repeated segments. A quick check of Wikipedia even suggests that 2/3rds of human DNA is composed of these repeating patterns. Repeating patterns like that, and particularly because they make up so much of our DNA, are ripe for compression.

I'm sure there are other aspects at play here, but those two facts in and of themselves pretty much guarantee that we can compress otherwise uncompressed binary representations of human DNA sequences.