As long as you have a passport or other proper documentation (check with the cruiseline as to what you need) the boarding process should not take any longer than if you were a US citizen. But if your comment was to the long line in general, the wait time depends on a lot of things. My advise is to show up early. You will have to wait until they start boarding, but if you are near the front of the line, once they start you can be right on board. If you show up after they start boarding and after the line has formed you will most likely wait longer that if you just showed up an on or so before they are supposed to begin boarding.
Carnival Cruise Lines:
Fantasy 90, Celebration 95, Victory 05, Conquest 05, Spirit 6/06, Freedom 6/08, Holiday 7/08, Victory 6/09, Valor 9/09, Dream 6/10, Splendor 8/10,Conquest 8/11,Magic 11/11,Triumph 4/12,Spirit 7/12,Freedom 11/12, Triumph 2/13 - The fire cruise, Magic 1/14
NCL Dream October 2006, RCCL Mariner OTS June 2007, Celebrity Silhouette 2013