if it's not easy to take a test quickly the difference in accumulated points between my son and most of the other kids will be reduced.
My DD was allowed to do AR in first grade (school starts in 2nd), and she found it very difficult to get test opportunities in.
Our school gives does AR as pass / fail, so missing a question doesn't interfere with points.
He's read a gazillion book and then he gets told to take a test. He's read so many books and the volunteer staff isn't that familiar with software and maybe my son can't spell the authors' names...so they end up deciding - OK, take one of the Harry Potter tests.
My DD had the book she wanted to test on with her, for "looking up test" purposes. Not getting the right test has never been an issue.
Her first grade teacher did warn us that in the grades where all the kids do AR, the teachers tend to limit the kids to at-grade-level or one-grade-up books. I'd asked if DD could test from any AR book she got from the school library, rather than having to use her one library book on a 1st or 2nd grade book.
With respect to "do other kids notice," first graders had reading logs - after you read a book, your parent recorded it in the log. I only gave DD "credit" for at-level books she'd read for the first time, and stopped writing books down once she'd filled her log for the month. She was disappointed that she didn't have the highest total at year-end (and if I'd known they were going to do totals, I'd have recorded more liberally), but it was a passing thing. And good for her to not automatically be on top.
