Probably not a bad idea, and not just for new immigrants. I think a lot of people would be surprised about what's in there and what's not in there. It's not that hard to read the document itself. The language is a bit dated, but clear. It's not written in "legalese" and it's not all that long, only about 8 pages in the NY Times Almanac. It might run about about 15-20 pages in larger print, especially if the inoperative parts are included and shown in italics or with a single line through the text (such as the part about slaves counting 3/5 of a person for the census). These parts, of course, have been superseded by amendments.
An interesting read for the beach on a hot summer day.