It was referred to outside Poland as Siedlitz and remember that this is a document made by an American official (notorious for garbling foreign place names and even surnames) rather than someone in Poland so it may be possible.
I do know there are people from Gdansk who share my last name but have no idea if we are relations. I'm working on that.
If it wasn't until 1918 that Poland was an independent country it's possible that his town had the old German spelling if he were born prior to that correct?
The changes to place names etc didn't happen overnight - they had a lot to do. Harry is right though - in the Russian zabór they wouldn't have used the German name of the town (unless it was the brief period during World War One that the Germans controlled the town, and even then probably not) but then again, the document you have isn't a Polish one.
Remember there were mass population movements and most of the pre-war inhabitants of Gdansk left at the end of the war or just after. The people there who share your surname may well have come from somewhere else. Have you seen the surname map on moikrewni.pl?