The puckering on the spine is due to the way the cover was glued to the pages. Pressing will not remove that. Good news is CGC considers that part of production. I have seen many high grade copies of this book with goofy spines.
As far as the pressing goes you cannot stay away from the staples, they are essentially on the cover. To the OP's comment, they are not misaligned, hey are where they should be. Someone who knows what they are doing can press this without causing additional damage. That's why you need to use someone reputable and with lots of experience. Having pressed hundreds of books is not a lot of experience. Ask if they have experience with square-bound books. Again, the staples affecting the covers is considered a production issue. I have worked on, and seen copies of this book with the staples popping through the cover get 9.4.
The short answer is yes, a proper dry cleaning and press will benefit this book. On a side note, always show both covers as we are making an assessment on only 50% of the comic