As a child of the Deep South, I love seersucker and the memories it invokes. In the days prior to "wash & wear", seersucker fit the bill. It felt good, looked good and lasted forever. Ironing was usually an all day job, starting with a full washtub of clothing that had been starched, sprinkled and rolled up to stay moist for ironing. With seer sucker there was always less ironing. If you could not get it all ironed that day, you put the sprinkled clothing in the freezer and waited for another day to iron. In those days it seemed to me that there was only one color, pale blue. When I watch an episode of "Matlock" and see his suits, it takes me back.
You asked about ironing out the puckers. I would say No, you cannot iron out the puckers because they were woven in.