You know what they say about "never say never."
But let me put it this way, I've never seen it done. The International has continuous turns, but they are natural spin turns and moves like the Whisk and chasse out of a promenade. The hold is never broken.
The underarm turn has been taught to me only as part of the American Smooth style; the same could be said for shadow twinkles and, possibly, grapevine steps. But the grapevine can be done without breaking ballroom position, and I actually like it better in that form.
But don't confuse holding position with just being able to do a box step. On the contrary, some of the most sweeping, elegant movements along LOD are done in ballroom position and International style.
Some of the ballroom historians who post on this site would know a lot more about it than I would, but I venture to guess that Fred Astaire had a lot to do with making American style well known as a more free-wheeling, open style -- and a place for him to spin and turn his partners magnificently -- knowing all along he could display great skill at the discipline and posture of International style as an overall part of his repetoire.