I’m not sure which hypothetical schools your are looking at.
There are often two types of scholarships awarded to National Merit students - one might be for NMSF or NMF and another (generally a smaller amount) is awarded when a student becomes a NMS.
Very few schools ask to be indicated as the first choice before May 1. BU is one of them and has a March 1 deadline. This post from last year might help answer your question.
To answer the last three posts, two months ago I contacted an admissions counselor at University #1, and they advised me to pick them as first choice by the end of February, as the students who get the larger scholarship will be almost for sure selected from the first batch of names they get from the NMSC on or very soon after March 1.
But it might. There are many people on this site who have asked the same question. I don’t have personal experience with all of the schools, but I have been on this board long enough that I might be able to direct you to where someone else found out the answer to the specific schools your are considering.
If you don’t want to state which schools you are looking at, and you don’t want to call NMSC, I suggest you look for the answer to your question in the threads from the Class of 2022, Class of 2023 and Class of 2024.
ETA: You can use the magnifying glass in the top right corner to search for references to a certain school in that thread.
I called the NMSC awhile ago but had a different experience than everyone else because to me they were useless. Maybe it was the person I got on the phone. Most likely my fault for not asking the question the right way.
But the posting with the BU example you sent to me nailed it right on the head. I can’t believe I didn’t see it before, I’ve read almost everything in here.
I’m hoping to update this thread with more information sometime in the summer.