Well anything is possible...If it's the big radiator, well, they are mounted differently, the mk1 is straight and the mk2 is at an angle and the nipples are different... You might want to look at this: http://www.vwdiesel.net/forum/index.php?topic=28329.0
he has a 81 jetta so correct bottom mount different... 82 jetta went to pins... 83 rabbit went to pins... not 84..
About all Mk2 AC radiators are gonna be way too wide for your 81 Jet.No harm in taking measurements to see for sure tho.I'd bet against it being an easy swap -but i've never seen a Non-AC Mk2 to even know what their radiators are like as far as width. in other matters - my 81 Truck has pins/grommets on lower mounts.not comparing it to a German built Jetta in any form - just adding to other semi-topic.