It’s possible, given that a day school, by definition, serves the community you live in, that you have a good idea of the kind of kids who have been admitted and attend (because you know many families there), what the school considers important, and how your kid stacks up against that. You may be closer to correct than you would be at a boarding school you have no affiliation with. But…
I recall a friend (applying from a k-8 private school) of a (local) boarding school DS applied to “We didn’t apply there. We just aren’t an xyz school type of family.” They weren’t and in spite of having two kids who ended up at Ivies, they were pretty sure they would just present as the square peg to the school’s round hole. I suspect they were right but I was pretty oblivious to this as we were going through the process (from a public school and with a more limited exposure to this.)
The piece you are missing is what all the other applicants look like. I recall being rather stunned by how accomplished many of my son’s freshmen classmates were. In different arenas, of course. But honestly, I had no idea so many kids with everything from Broadway experience to state championships in sports, to math competition wins were even in the pool because there were NONE of these in his middle school.
I wasn’t terribly surprised at the outcomes, but I wasn’t completely correct either…