Depends which schools you are talking about. (These are business schools - not colleges).
Round 3 in top 20 in the US is always a bad round to apply for, no matter who you are and where you are from. The reason is that acceptance rates are very low since schools have filled up with the people they wanted to admit. Some even prevent international applicants from applying in R3.
If it is a top 50 or 100, then it is a different story as their deadlines are much more shifted out. However, another weakness of R3 is the lack of scholarship funds remaining; they are usually reserved for only truly outstanding applicants.
However, there is not really many downsides to trying besides putting in a lot of effort.