There are an infinite number of points that are "abeam point B". If we understand your question, you're proposing to travel via the one point that's "abeam point B" and is also on the great circle from A to C. So you're always on the great circle, if you (or the machine) calculated the lat-lon of that point correctly. Are you asking whether you can trust the machine to do that?
If that's what you're wondering, there are calculators on the web you can use to check the machine.