I assume we're talking about merit scholarships.
Will some other applicants be putting it on their application? Yes.
Does that give them a competitive edge over you? At most a tiny tiny bit. PDs have 101 things that are more important.
Do some schools put it on the Dean's letter? Yes. My school's deans letter will note that you majored in biology at Harvard and graduated PBK and magna cum laude, and entered medical school as a distinguished student scholar, or something like that.
Will it hurt you to put it? No. PDs tend to always want more information than not. This is like the debate about preclinical grades. On one hand, PDs say preclinical grades are 'somewhat important' (3 out of 5) and past surveys have shown that PDs would greatly prefer to see preclinical grades than a pass/fail transcript. On the other hand, ranked against 15-30 other factors considered in resident selection, preclinical grades falls in the bottom quartile in terms of importance. Somehow you have to reconcile that this is important on an absolute scale but not on a relative scale.
Why is this relevant? A merit scholarship indicates that 1) you were recruited to some extent, and 2) you entered as one of the top students. The former is relevant in case you go to some less prestigious school than your premed credentials might give you credit for. School name matters a little. So a scholarship is a bit of an excuse in that area. The latter is relevant because if you are going into residency applications as an AOA student, that in conjunction with the scholarship demonstrates you have a long-term history of excellence compared to your peers.
Will people actually be thinking that? Probably not. It's possible though.
Do residencies care about undergraduate/college stuff? Probably only a little, if at all. Most surveys of PDs do not ask about undergrad stuff. When it is asked, it's rated like a
4.8 out of 10 (as important to ortho programs as being an MD/PhD), lower than most factors. That said, ERAS has a place for you to upload undergraduate transcripts. Most programs don't require this, but
some competitive programs do. SF match (ophtho) requires it.
Why would they care about undergrad stuff? 1) As stated above, they want a demonstrated history of sustained excellence. 2) They look for any way possible to stratify applicants. Is the fact that you went to Harvard rather than Podunk U for undergrad going to make a difference? Probably not.
Is this like putting down your MCAT? A little. Again,
the occasional residency programs require your MCAT score. I presume it's along the same reasoning as above (history, stratification). However, the MCAT is a little different because, as a standardized test of knowledge, it gets overshadowed and superceded by Step 1. The achievements that lead you to getting a merit scholarship are different, more comprehensive, less defined, and do not get directly superceded by a more proximal measure.