I think it would probably depend on the school.
I live in an urban area- and prep schools are not generally need blind. Those with need may be waitlisted just because they are putting together a class- and the more students that are full pay, the more flexibilty then they would have when finding the students to fill the aid slots.
( not saying you have need- I am speaking in general)
My oldest applied to 5 prep schools for 6th grade. ( and at the time it was
such a process I thought " boy, by the time she applies to colleges- she will be able to do this all herself! " Bwahaha!

)
One school- was K-12, so very few slots as most either had already been attending, or had siblings already attending.
Two other schools also began in 5th grade, so very few slots for 6th graders.
She was admitted to one school, which was probably last choice and waitlisted at what was close to first choice.
She was ( is) a very cute and perky blond girl, very bright- but had lots of financial need. We couldn't even think of her attending unless the schools had given her a big grant.
Very cute & perky blond girls who are very bright are frankly a dime a dozen. When a class is only 15 students or so, it gets competitive. You can't have the whole classroom made up of bubbly females, you need room for sports fixated boys and girls, geeks who can upgrade the servers, gifted musicians and future politicians.
Your son may already have his description filled in the class by a currently attending sibling.
However,- I had. had a very nice long chat with the admissions director at the school where she was waitlisted ( while D was touring- long before decisions were made) and I felt very good about the school.
After the tour, we ( I ) sent a thank you card to the school & when she was waitlisted we sent a note saying that she still liked it very much and was hoping to attend.
She was admitted and with the aid she needed and she attended through senior year.
I don't know what it is like in your area- I know that in our area, we have fewer seats for more students- but letting them know that you are still interested can't hurt.