I've got a 12 in auger for my BX 2370. I think I could handle a bit bigger but that was the largest they had when I picked it up, a 18 would probably be a bit much. The biggest Issue is that the tip of the auger will drag on any little bump because there is just not enough lift in the 3 point.
For reference I've got hard wet heavy clay. I do need to make sure that I clear the hole regularly, especially with my extension installed. Last weekend I dug footings for my new deck, one got stuck and it sucked into the hole. A little shovel work and a chain on my loader got it out without too much work. The rest went fine after I realized I needed to clear the holes often. While running the auger I was just over idle, never needed more power.
pgmrdan, this is the third post I've see you asking about if a BX can handle something. In the year I've had my BX 2370 I've yet to find something I can't do, just a few things that take a bit longer, usually it is traction or loader capacity that is the limiting factor, not power. While there are those out there who disagree but a BX IS a tractor, and can get a lot of work done, I've even started to see them on highway construction jobs once an a while (specialty contractors not the dirt guys). Don't baby your machine too much, they would rather work, and do it well.